Home
Class 12
MATHS
y(x^(2)y+e^(x))dx-e^(x)dy=0...

`y(x^(2)y+e^(x))dx-e^(x)dy=0`

Text Solution

Verified by Experts

The correct Answer is:
`x^(3)y+3e^(x)=cy`
`y(x^(2)y+e^(x))dx-e^(x)dy=0`
or `ye^(x)dx-e^(x)dy+x^(2)y^(2)dx=0`
or `(ye^(x)dx-e^(x)dy)/(y^(2))+x^(2)dx=0`
`d(e^(x)y)+x^(2)dx=0`
Integrating, we get
`e^(x)/y+x^(3)/3=k`
or `x^(3)y+3e^(x)=3ky`
or `x^(3)y+3e^(x)=Cy`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISES 10.6|7 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISES 10.7|5 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISES 10.4|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

y(2x y+e^x)dx-e^x dy=0

Solution of the differential equation y(a x y+e^x)dx-e^x dy=0 where y(0)=1 is

(b) Solve: (x.e^(xy)+2y)dy+y.e^(xy)dx=0

The solution of the differential equation (dy)/(dx) = e^(x-y) (e^(x)-e^(y)) is

The solution of y e^(-x/y)dx-(x e^((-x/y))+y^3)dy=0 is

Solve the following differential equations: y e^(x//y)dx=(x e^(x/y)+y)dy

Solve the following differential equation: (1+e^(x//y))dx+e^(x//y)(1-x/y)dy=0

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

Solve y e^(x/y)dx=(x e^(x/y)+y^2)dy ,(y!=0)dot

Solve (1+2e^(x//y))dx+2e^(x//y)(1-x//y)dy=0.