Home
Class 12
MATHS
Solve : (x+2y^3)dy/dx=y...

Solve : `(x+2y^3)dy/dx=y`

Text Solution

Verified by Experts

This equation can be rewritten as
`(dx)/(dy) = 1/yx+2y^(2)`
or `(dx)/(dy) -1/y.x=2y^(2)`.
This is linear differential equation of the form `(dx)/(dy)+Px=Q`, where P and Q are function of y.
Here, I.F.`e^(-int1/ydy)= e^(-logy)=1/y`
`therefore` Solution is `x1/y=int1/y2y^(2)dy+C`
`rArr x/y=y^(2)+C`
`rArr x=y^(3)=cy`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise EXAMPLES|18 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISES 10.1|6 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Solve: (x-y^3)(dy)/(dx)+y=0

solve: (y-x)(dy)/(dx)=y

Solve: (x-y)(dy)/(dx)=x+3y

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

Solve: (x-y)^2(dy)/(dx)=a^2

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

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

Solve: y^(4)dx+2xy^(3)dy=(ydx-xdy)/(x^(3)y^(3))

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

Solve: y\ dx-(x+2y^2)dy=0