1.

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

Answer»

`2sqrt3`
`3sqrte`
`4sqrte`
`6sqrte`

Solution :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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