Originally Posted by

**TrevorP** Hey,

I've been having some trouble recreating the answer my teacher has for the following question:

Find $\displaystyle y(x)$ given $\displaystyle \frac{dy}{dx} = x^3y$, where $\displaystyle y(1) = 2$.

So I did the following:

$\displaystyle \int \frac{dy}{y} = \int x^3dx \longrightarrow \ln{y} = \frac{x^4}{4} + C$

$\displaystyle y = e^{\frac{x^4}{4} + C} \ \ or \ \ y = Ce^{\frac{x^4}{4}}$

Where C is some constant to be solved for.

Anyway I could solve for C. But what is getting me is that my prof's final answer is:

$\displaystyle y = 2e^{\frac{x^4}{4} - \frac{1}{4}}$

Which would mean there was two constants...but I would need more initial conditions for that.