[SOLVED] First order non linear non homogeneous DE

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March 3rd 2010, 10:15 AM
arbolis

[SOLVED] First order non linear non homogeneous DE

I must solve the following DE: $x'(x-x^2)=t+t^2$ .
My attempt: $(x-x^2)dx=(t+t^2)dt \Rightarrow x^2 \left ( \frac{1}{2}-\frac{x}{3} \right)= t^2 \left ( \frac{1}{2}+\frac{t}{3} \right ) +C$ . I feel I'm on the wrong direction. How would you tackle it?
March 3rd 2010, 11:19 AM
chisigma

In my opinion You are proceeding in the right direction!... what You have to do now is to find an explicit expression of x as function of t by resolving the algebraic equation...

$\frac{x^{2}}{2} - \frac{x^{3}}{3} - \frac{t^{2}}{2} - \frac{t^{3}}{3} + c = 0$ (1)

The (1) is a third order equation so that You obtain [in general...] three different solution and among them the 'right' solution is determined [when possible...] by the 'initial conditions'...

Kind regards

$\chi$ $\sigma$

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