Home
Class 12
MATHS
The solution of the differential equatio...

The solution of the differential equation `ydx+ (x +x^2 y) dy =0` is

Text Solution

Verified by Experts

The correct Answer is:
`-1/(xy)+log_(e)y=c`
`ydx+(x+x^(2)y)dy=0`
or `(xdy+ydx)+x^(2)ydy=0`
or `d(xy)+x^(2)ydy=0`
or `(d(xy))/(xy)^(2)+1/ydy=0`
Integrating, we get `-1/xy+logy=c`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.6|7 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.7|5 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.4|6 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

The solution of differential equation 4xdy - ydx = x^(2) dy is

The solution of the differential equation ydx-(x+2y^(2))dy=0 is x=f(y). If f(-1)=1, then f(1) is equal to

The solution of differential equation ydx + (x+xy)dy = 0 is

The general solution of the differential equation ydx+(x+2y^(2))dy=0 is

Solution of the differential equation y dx+(x-y^(2))dy=0 is

(i) The degree of the differential equation (d^(2)y)/(dx^(2))+e^(dy//dx)=0 is… (ii) The degree of the differential equation sqrt(1+((dy)/(dx))^(2))="x is"....... (iii) The number of arbitrary constant in the general solution of differential equation of order three is.. (iv) (dy)/(dx)+(y)/(x log x)=(1)/(x) is an equation of the type.... (v) General solution of the differential equation of the type is givven by... (vi) The solution of the differential (xdy)/(dx)+2y=x^(2) is.... (vii) The solution of (1+x^(2))(dy)/(dx)+2xy-4xy^(2)=0 is... (viii) The solution of the differential equation ydx+(x+y)dy=0 is .... (ix) Genergal solution of (dy)/dx)+y=sin x is.... (x) The solution of differential equation cot y dx=xdy is.... (xi) The integrating factor of (dy)/(dx)+y=(1+y)/(x) is.....

If x=x(y) is the solution of the differential equation, ydx-(x+2y^2)dy=0 , with x(-pi)=pi^2 , then x is equal to :