Home
Class 12
MATHS
Find a particular solution of the diffe...

Find a particular solution of the differential equation `(x+1)(dy)/(dx)=2e^(-y)-1`given that `y = 0`when`x = 0`.

Text Solution

Verified by Experts

Given,
`=>((x+1)dy​)/(dx)=2e^(−y)−1`
`=>(dy)/(2e^(−y)−1)=(dx)/(x+1)`
`=>(dy)/(2e^(−y)−1)=ln(x+1)+c`
Let `t=2e^(−y)−1`
So, `dt=−2e^(−y)dy`
So,from equation,
`=>(-dt)/(t(t+1))=ln(x+1)+c`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Find the particular solution of the differential equation (dy)/(dx)=-4xy^(2) given that y=1, when x=0

Find the particular solution of the differential equation x(dy)/(dx) - y = (x + 1 ) e^(-x) given that y = 0 when x = 1 .

Find the particular4solution of the differential equation (x-y)(dy)/(dx)=x+2y, given that when x=1,y=0

Find the particular solution of the differential equation x(x^(2)-1)(dy)/(dx) =1, it being given that y = 0 when x = 2.

Find the particular solution of the differential equation (dy)/(dx) = 1+x+y+xy, given that y = 0 when x = 1.

Find the particular solution of the differential equation log((dy)/(dx))=3x+4y given that y=0 when x=0

Find the particular solution of the differential equation (dy)/(dx)=(y(2y-x))/(x(2y+x)) ,given that y=1 when x=1 .

Find the particular solution of the differential equation (dy)/(dx)=-4xy^(2) given that given that when x=0

Find the particular solution of the differential equation x(dy)/(dx)=y+x cosec ((y)/(x))=0; given that y=0 when x=1