# Thread: [SOLVED] Find DE given slope and point?

1. ## [SOLVED] Find DE given slope and point?

Find the equation of the curve that passes thru the point (0,1) & whose slope at (x,y) is 13xy.

I'm not sure how to start this. Can someone get me started without doing the whole prob?
Thanks

2. $\frac{dy}{dx} = 13xy$

separate variables ...

$\frac{dy}{y} = 13x \, dx$

integrate ...

$\ln|y| = \frac{13x^2}{2} + C_1$

$y = C_2e^{\frac{13x^2}{2}}$

$y(0) = 1$

$1 = C_2e^0$

$C_2 = 1$

$y = e^{\frac{13x^2}{2}}$