Simple and best practice solution for (Xy^2x)dx(yx^2y)dy=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homeworkCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historySolution for y^2dx (x^2xy)dy=0 equation Simplifying y 2 dx (x 2 1xy) * dy = 0 Reorder the terms dxy 2 (1xy x 2) * dy = 0 Reorder the terms for easier multiplication dxy 2 * dy (1xy x 2) = 0 Multiply dxy 2 * dy d 2 xy 3 (1xy x 2) = 0 (1xy * d 2 xy 3 x 2 * d 2 xy 3) = 0 (1d 2 x 2 y 4 d 2 x 3 y 3) = 0 Solving 1d 2 x 2 y 4 d 2 x 3 y 3 = 0 Solving for variable 'd'
Homogeneous Equations
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X 2 y 2 dx x 2-xy dy 0 homogeneous-Solve the following differential equation (x2 y2)dx 2xy dy = 0 (i) Prove that the DE is (3xy y^2) dx (x^2 xy) dy = 0 a homogeneous DE of degree 0 (ii) Solve the DE (3xy y^2) dx (x^2 xy) dy = 0 asked Jan 19 in Differential Equations by Raaida ( 297k points)
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Avail 25% off on study pack2x 3 d x 2 y 2 d = x 2 d • (2x y 2) Equation at the end of step 8 x 2 d • (2x y 2) = 0 Step 9 Theory Roots of a product 91 A product of several terms equals zero When a product of two or more terms equals zero, then at least one of the terms mustHomogeneous Differential Equations A first order Differential Equation is Homogeneous when it can be in this form dy dx = F ( y x ) We can solve it using Separation of Variables but first we create a new variable v = y x v = y x which is also y = vx And dy dx = d (vx) dx = v dx dx x dv dx
113k views asked in Class XII Maths by nikita74 (1,017 points) Find the general solution of y 2 dx (x 2 xyy 2 )dy = 0 differential equations We can rearrange this Differential Equation as follows dy dx = − x2 y2 x2 − xy = − ( 1 x2)(x2 y2) ( 1 x2)(x2 −xy) = − 1 ( y x)2 1 − y x So Let us try a substitution, Let v = y x ⇒ y = vx Then dy dx = v x dv dx And substituting into the above DE, to eliminate yHomogeneous Differential Equation (y^2 yx)dx x^2dy = 0If you enjoyed this video please consider liking, sharing, and subscribingYou can also help suppor
Results Problem 03 (2xy − 3x2)dx (x2 y)dy = 0 Solution 03 Show Click here to show or hide the solution ( 2 x y − 3 x 2) d x ( x 2 y) d y = 0 M = 2 x y − 3 x 2 N = x 2 yFirst order homogeneous differential equation is the one which can be expressed as dy dx = f(y x) d y d x = f ( y x) It can then be solved by substituting v = y x, v = y x, which makes it a Find the general solution of y^2dx (x^2 – xy y^2) dy = 0 asked in Differential Equations by Chandan01 ( 512k points) differential equations
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Answer to Solve the Homogeneous equation (x^2y^2 )dx(x^2−xy)dy = 0 Get 11 help now from expert Advanced Math tutorsActive 6 years, 1 month ago Viewed 4k times 2 Find the general solution to the homogeneous differential equation ( x 2 − y 2) d x ( 3 x y) d y = 0 The differential equation does not seem to be separable, and I'm having a tough time to put it in the general form of d y d x p ( x) y = f ( x)Subproblem 2 Set the factor ' (y 2x)' equal to zero and attempt to solve Simplifying y 2x = 0 Reorder the terms 2x y = 0 Solving 2x y = 0 Move all terms containing d to the left, all other terms to the right
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The differential equation is given as, x2dy(y2−xy)dx = 0 x 2 d y ( y 2 − x y) d x = 0 To find the solution of differential equation, Rewrite the given equation as, x2dy(y2−xy)dx= 0 Ex 95, 12 For each of the differential equations in Exercises from 11 to 15 , find the particular solution satisfying the given condition 𝑥2𝑑𝑦 𝑥𝑦 𝑦2 𝑑𝑥=0;𝑦=1 When 𝑥=1 The differential equation can be written 𝑎s 𝑥2𝑑𝑦 = −(xy y2) dx 𝑑𝑦𝑑𝑥 = − 𝑥𝑦 𝑦2 𝑥2 LetStack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange
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I'm at the beggining of a differential equations course, and I'm stuck solving this equation $$(x^2y^2)dx2xy\ dy=0$$ I'm asked to solve it using 2 different methods I proved I can find integrating factors of type $\mu_1(x)$ and $\mu_2(y/x)$If I'm not wrong, these two integrating factors are $$\mu_1(x)=x^{2} \ \ , \ \ \mu_2(y/x)=\left(1\frac{y^2}{x^2}\right)^{(x^2 y^2)*dx 2*x*y*dy = 0 Go to polar coordinates x = r*cos(a), dx = cos(a)*dr r*sin(a)*da y = r*sin(a), dy = sin(a)*dr r*cos(a)*da Your equation now becomes cos(a)*dr r*sin(a)*da = cos(a)*sin(a)*(sin(a)*dr r*cos(a)*da y^2 = x^2(2lnx c) We can rewrite this Ordinary Differential Equation in differential form (x^2 y^2) \ dx xy \ dy = 0 A as follows \ \ \ \ dy/dx = (x^2 y^2)/(xy) dy/dx = x/y y/x B Leading to a suggestion of a substitution of the form u = y/x iff y = ux And differentiating wrt x whilst applying the product rule dy/dx = u x(du)/dx Substituting into the DE B
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Solution of the differential equation `(x^(2)y^(2))dx2xy dy=0` isSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreAnswer to Solve the differential equation (x^2 2(y^2))dx (xy)dy = 0 By signing up, you'll get thousands of stepbystep solutions to your
Homogeneous Equations
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# dy/dx = (x^2y^2xy)/x^2 # with #y(1)=0# Which is a First Order Nonlinear Ordinary Differential Equation Let us attempt a substitution of the form # y = vx # Differentiating wrt #x# and applying the product rule, we get # dy/dx = v x(dv)/dx # Substituting into the initial ODE we get # v x(dv)/dx = (x^2(vx)^2x(vx))/x^2 #Find dy/dx x^2y^2=2xy Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps Differentiate Tap for more steps By the Sum Rule, the derivative of with respect to is Differentiate using the Power Rule which states that is where Transcript Ex 95, 4 show that the given differential equation is homogeneous and solve each of them ( ^2 ^2 ) 2 =0 Step 1 Find / ( ^2 ^2 ) 2 =0 2xy dy = ( ^2 ^2 ) dx 2xy dy = ( ^2 ^2 ) dx / = ( ^2 ^2)/2 Step 2 Putting F (x, y) = / and finding F ( x, y) F (x, y) = ( ^2 ^2)/2 F ( x, y) = ( ( )^2 ( )^2)/ (2 )= ( ^2 ^2 ^2 ^2)/ ( ^22 )= ( ^2 ( ^2 ^2))/ ( ^22 ) = ( ^2 ^2)/2 = F (x, y) F ( x, y) = F (x,
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Click here👆to get an answer to your question ️ Solve (x^2 y^2)dx xydy = 0 find the particular solution of given differential equation 3xy y 2 dx x 2 xy dy 0 at x 1 y 1 Mathematics TopperLearningcom d1ksg633 Starting early can help you score better!Solve ( dy(x))/( dx) (x x^2 y(x)^2) x y(x)^2 y(x) = 0 Let y(x) = sqrt(v(x))/x, which gives ( dy(x))/( dx) = sqrt(v(x))/x^2 (( dv(x))/( dx))/(2 x sqrt(v(x))) (x v(x)) (sqrt(v(x))/x^2 (( dv(x))/( dx))/(2 x sqrt(v(x)))) sqrt(v(x))/x v(x)/x = 0 Simplify
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Derivatives Solve the differential equation $ (y^2xy)dxx^2dy=0$ Mathematics Stack ExchangeSimple and best practice solution for (x^2y^2x)dx(xy)dy=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homeworkFor the differential equation `(x^2y^2)dx2xy dy=0`, which of the following are true (A) solution is `x^2y^2=cx` (B) `x^2y^2=cx` `x^2y^2=xc` (D) `y
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Show that the given differential equation is homogeneous x^2(dy/dx) = x^2 2y^2 xy askedin Differential Equationsby KumkumBharti(539kpoints) differential equations class12 0votes 1answer Show that the differential equation (x y) (dy)/dx = x 2y is homogeneous and solve itDivided by "y^2" (2x/y1)dx(x^2/y^2x/y)dy=0 Z= x/y → x= yz → dx=zdy ydz (2z1)dx(z^2z)dy=0 (2z1)(zdyydz)(z^2z)dy=0 (2z^2z)dyy(2z1)dz(z^2z)dy=0 (z^2)dyy(2z1)dz=0 (1/y)dy=(2z1)/z^2 dz (1/y)dy=(2/z1/z^2)dz Lny= 2lnz 1/z c Lny 2 lnz =1/z c Ln(y*z^2)=(1/z) c y*(x/y)^2= e^(y/x)c= e^(y/x)* e^c X^2/y = C* e^(y/x) where C=To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Show that the differential equation ` (dy)/(dx) = y^2/ (xy x^2)` is homogeneou
Ordinary Differential Equations
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2 y (x) (2 x y (x) 4) ( dy (x))/ ( dx) = 0 Let R (x, y) = y 2 and S (x, y) = 2 x y 4 This is not an exact equation, because (dR (x, y))/ (dy) = 1!=2 = (dS (x, y))/ (dx) Find an integrating factor μ (y) such that μ (y) R (x, y) ( dy (x))/ ( dx) μ (y) S (x, y) = 0 is exactHomogeneous Equations Given equation (3x2−y2)dx(xy−x3y−1)dy = 0 ( 3 x 2 − y 2) d x ( x y − x 3 y − 1) d y = 0 We can write this equation as follows dy dx = x3−xy2 3x2y−y3Click here👆to get an answer to your question ️ Solve the differential equation, (x^2 xy)dy = (x^2 y^2) dx
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N = x^2 xy^2 , N_x = 2x y^2 # M_y The equation is not exact but (N_x M_y)/M = 2/y , depends only on y The integrating factor 1/y^2 leads to the equation P(x,y)dx Q(x,y)dy =0,with P = 2x/y y , P_y = 2x/y^2 1 Q = x^2/y^2 x , Q_x = 2x/y^2 1 = M_y This equation is exact and is the total differential dF(x,y) =0 solvedSolve ( dy (x))/ ( dx) (x x^2 y (x)^2) x y (x)^2 y (x) = 0 Let y (x) = sqrt (v (x))/x, which gives ( dy (x))/ ( dx) = sqrt (v (x))/x^2 ( ( dv (x))/ ( dx))/ (2 x sqrt (v (x))) (x v (x)) (sqrt (v (x))/x^2 ( ( dv (x))/ ( dx))/ (2 x sqrt (v (x)))) sqrt (v (x))/x v (x)/x = 0 Simplify 1 Answer1 Active Oldest Votes 1 ( x y) d x − ( x 2 y 2) d y = 0 Let F ( x, y) = x y and let G ( x, y) = x 2 y 2 Now consider a function u ( x, y) = 0 Then ∂ u ∂ x d x
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Solution for (y^2xy)dxx^2dy=0 equation Simplifying (y 2 xy) * dx x 2 dy = 0 Reorder the terms (xy y 2) * dx x 2 dy = 0 Reorder the terms for easier multiplication dx (xy y 2) x 2 dy = 0 (xy * dx y 2 * dx) x 2 dy = 0 Reorder the terms (dxy 2 dx 2 y) x 2 dy = 0 (dxy 2 dx 2 y) x 2 dy = 0 Combine like terms dx 2 y dx 2 y = 2dx 2 y dxy 2 2dx 2 y = 0 Solving dxy 2 answered by Sarita01 (535k points) selected by AmanYadav Best answer Answer is (A) x2(2xy y2) = c2 It can be written in the form of homogeneous equation Hence, the required solution is x2(2xy y2) = c2 Please log in or register to add a comment ← Prev Question Next Question →Question (x^2y^2)dx(x^2xy)dy=0 , solve this equation as Homogeneous substitution This question hasn't been solved yet Ask an expert Ask an expert Ask an expert done loading
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If the given curve satisfies the differential equation e y d x (x e y 2 y) d y = 0 and also passes through (0, 0) the possible equation of curve can be Medium View solution
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