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If the solution of the differential equa...

If the solution of the differential equation `(dy)/(dx)-y((x^4+3x^2)/((x^2+1)^2))=(4x+3)e^(x^3/(x^2+1)` is in the form y=f(x) (where f(0)=1), then f(A)+f(-1) is

A

`2sqrt3`

B

`3sqrte`

C

`4sqrte`

D

`6sqrte`

Text Solution

Verified by Experts

The correct Answer is:
D
I.F.=`e^(-int(x^4+3x^2)/((x^2+1)^2) dx = e^((-x^3)/(x^2+1))`
`rArr y e^((-x^3)/(x^2+1))=int(4x+3)dx`
`rArr f(x)=y=(2x^2 + 3x +1)e^((x^3)/(x^2+1))`
`rArr f(1)=6sqrte` & f(-1)=0
`rArr` f(-1)=0
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