Home
Class 12
MATHS
(dy)/(dx)=(2xy)/(x^(2)-y^(2))...

`(dy)/(dx)=(2xy)/(x^(2)-y^(2))`

Text Solution

Verified by Experts

The correct Answer is:
`(x^(2)+2y^(2))^(3)=Cx^(2)`
`x(dv)/(dx)=-(1+2v^(2))/(3v)=int(3v)/(1+2v^(2))dv =-int1/xdx`
`rArr 3/4int(4v)/(1+2v^(2))dv=-int1/xdx rArr 3/4log|1+2v^(2)|+log|x|=log|C_(1)|`.
Promotional Banner

Topper's Solved these Questions

  • HOMOGENEOUS DIFFERENTIAL EQUATION

    RS AGGARWAL|Exercise Exercise 20|30 Videos

  • FUNDAMENTAL CONCEPTS OF 3-DIMENSIONAL GEOMETRY

    RS AGGARWAL|Exercise Exercise|18 Videos

  • INDEFINITE INTEGRAL

    RS AGGARWAL|Exercise Objective Questions|41 Videos

Similar Questions

Explore conceptually related problems

The solution of the differential equation (dy)/(dx)=(xy)/(x^(2)+y^(2)) is

STATEMENT -1 : The differential equation (dy)/(dx) = (2xy)/(x^(2) + y^(2)) Can't be solved by the substitution x = vy. and STATEMENT-2 : When the differential equation is homogeneous of first order and first degree, then the substitution that solves the equation is y = vx.

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

(dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2))

(dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2))

Solve (dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2))

The straight line y=2x meets y=f(x) at P, where f(x) is a solution of the differential equation (dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2)) such that f(1)=3 , then f'(x) at point P is

If the straight line y=x meets y=f(x) at P, where f(x) is a solution of the differential equation (dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2)) such that f(1)=3 , then the value of f'(x) at the point P is

(dy)/(dx)=(x^(2)-y^(2))/(xy)