- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

Let f be a real valued differentiable function defined in (-1,1). If f(0)=2 and [itex]f'(x)=f(x)+e^x(\sqrt{x^4+1})[/itex] , then find [itex]\frac{df^{-1}(x)}{dx}[/itex] at x=2.

## Homework Equations

## The Attempt at a Solution

[itex]\frac{dy}{dx}=y+e^x \sqrt{x^4+1} \\

dy=(y+e^x \sqrt{x^4+1})dx[/itex]

Integrating both sides

[itex]y=xy+\int (e^x\sqrt{x^4+1})dx[/itex]

I don't know the integration ahead.