Home
Class 12
MATHS
The solution of (dy)/(dx)+y=e^(-x), y(0)...

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

A

`y=e^(x)(x-1)`

B

`y=xe^(-x)`

C

`y=xe^(-x)+1`

D

`y=(x+1)e^(-x)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that, `" "(dy)/(dx)+y=e^(-x)`
Here, `" "P=1, Q=e^(-x)`
`" "IF=e^(intPdx)=e^(intdx)=e^(x)`
The general solution is
`" "y*e^(x)=inte^(-x)e^(x)dx+C`
`rArr" "y*e^(x)=intdx+C`
`rArr" "y*e^(x)=x+C" "` ...(i)
When x = 0 and y = 0, then
`" "0=0+CrArrC=0`
Eq. (i) becomes `" "y*e^(x)=x`
`rArr" "y=xe^(-x)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The solution of x(dy)/(dx)+y=e^(x)"is"

The solution of (dy)/(dx)+P(x)y=0 , is

The solution of (dy)/(dx)-y=1, y(0)=1 is given by

The solution of (1+x)(dy)/(dx)+1=e^(x-y) is

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

A particular solution of log ( dy //dx) = 3x + 5y, y(0) =0 is :

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

Solve the following initial value problem: (dy)/(dx)+2y=e^(-2x)sinx ,\ y\ (0)=0

Let y=f(x) is a solution of differential equation e^(y)((dy)/(dx)-1)=e^(x) and f(0)=0 then f(1) is equal to

For each of the following initial value problems verify that the accompanying functions is a solution. (i) x(dy)/(dx)=1,\ y(1)=0 => y=logx (ii) (dy)/(dx)=y ,\ y(0)=1 => y=e^x (iii) (d^2y)/(dx^2)+y=0,\ y(0)=0,\ y^(prime)(0)=1 => y=sinx (iv) (d^2y)/(dx^2)-(dy)/(dx)=0,\ y(0)=2,\ y^(prime)(0)=1 => y=e^x+1