Solve the initial value problem

[dashkin111]

Homework Statement

Solve the initial value problem given x(2)=0

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

Homework Equations

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?

 

[Dick]

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

 

[dashkin111]

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

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