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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))/(e^(2)+1))` is in the form y `=f(x)` (where `f(0)=1`), then `f(A)+f(-1)` is

A

`2sqrt(e)`

B

`3sqrt(e)`

C

`4sqrt(e)`

D

`6sqrt(e)`

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))`
`impliesye^((-x^(5))/(x^(2)+1))=int(4x+3)dx`
`impliesf(x)=y=(2x^(2)+3x+1)e^((x^(3))/(x^(2)+1)`
`impliesf(1)=6sqrt(e)` & `f(-1)=0`
`impliesf(-1)=0`
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