solution to the differential equation: dy/dx= xy

[ucci]

How do I find the solution to the differential equation: dy/dx= xy

Please break down the work into step and specify any rules used to solve the problem.

Here's the work I've done so far:

dx * (dy/dx)= xy(dx)

dy *(1/y) = (xydx/y)

dy *(1/y)= (d/dx)x

dy *(1/y)= (1/2)x^2

ln(y)= (1/2)x^2

Thank you,

Ucci

 

[galactus]

Lookin' good so far. You forgot your constant c on the right, though.

Just take e to both sides to solve for y.

\(\displaystyle e^{ln(y)}=e^{\frac{x^{2}}{2}+c}\)

\(\displaystyle y=e^{\frac{x^{2}}{2}}e^{c}\)

But \(\displaystyle e^{c}\) is a constant which we can represent by C

\(\displaystyle y=Ce^{\frac{x^{2}}{2}}\)

 

[ucci]

Thank you sooo much!