1.

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

Answer»

`2sqrt(E)`
`3sqrt(e)`
`4sqrt(e)`
`6sqrt(e)`

Solution :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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