Solve the initial value problem

1. Oct 8, 2007

dashkin111

1. The problem statement, all variables and given/known data
Solve the initial value problem given x(2)=0

$$\frac{dx}{dt}=tx^{2}+2x^{2}t^{2}$$

2. Relevant equations

3. The attempt at a solution
I factored out the x^2 and separated variables and integrated as follows:

$$\int\frac{dx}{x^{2}} = \int t+2t^{2} dt$$

$$\frac{-1}{x}=\frac{1}{2}t^{2}+\frac{2}{3}t^{3} + C$$

Which is simple enough, but I get really confused when solving for C. Trying to solve from the equation above divides by zero and the world ends- rearranging explicitly for x doesn't do me any good either. Suggestions on where to go from here?

2. Oct 8, 2007

Dick

This may seem like kind of a cheat, but x(t)=0 for all t is also a solution.

3. Oct 8, 2007

dashkin111

Thanks for that, I didn't think of that case. If something similar shows up on the exam I'll always check for something like that

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