Home
Class 12
MATHS
If the solution of the differential equa...

If the solution of the differential equation `(dy)/(dx)-y=1-e^(-x)` and `y(0)=y_0` has a finite value, when `xvecoo,` then the value of `|2/(y_0)|` is__

Text Solution

Verified by Experts

The correct Answer is:
4
`(dy)/(dx) -y=1-e^(-x)`
`P=-1,Q=1-e^(-x)`
I.F`. E^(intPdx)=e^(int-1dx)=e^(-x)`
`therefore y.e^(-x)=inte^(-x)(1-e^(-x))dx+C`
`=e^(-x)+1/2e^(-2x)+C`
When, `x=0, y=y_(0)+1/2`
So, `C=y_(0)+1/2`
`y=-1+1/2e^(-x) +(y_(0)+1//2)e^(x)`
When `x to infty y` takes finite value.
So, `y_(0)+1//2=0`
or `y_(0)=-1//2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Matrix Match Type|3 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

If the solution of the differential equation (dy)/(dx)-y=1-e^(-x) and y(0)=y_(0) has a finite value,when x rarr oo, then the value of |(2)/(y_(0))| is _(-)

The solution of the differential equation e^(2dy/dx)=x+1,y(0)=0 is

Solution of the differential equation 1+(dy)/(dx)+cosec(x+y)=0 is

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2) , when y(0)=1 is

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

The solution of the differential equation (2x-4y+3)(dy)/(dx)+(x-2y+1)=0 is

Solution of the differential equation (x+y-1)dx+(2x+2y-3)dy=0 is