- #1

- 18

- 0

## Homework Statement

We consider the solution to the differential equation x'(t)=-x(t)+atx(t)

^{2}, x(0)=e as a function of the variable a. Define d/da x(t,a)

_{t=1, a=0}

## Homework Equations

## The Attempt at a Solution

I suppose the differentiation won't be too hard, but my problem is I just don't get a solution xt,a) to the equation. I've tried splitting x'(t) into dx/dt, but that didn't work, and in desperation I've tried a number of random (ok they are not random, because I have still given it some thouht but I haven't used any special method) functions involving e, sin or cos. This is actually the part of the course that's dealing with systems of differential equation, so I've forgotten some of the stuff we learnt about this type of equations about a year ago. I hope you can help!