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
$\displaystyle \frac{dy}{dx} = 13xy$
separate variables ...
$\displaystyle \frac{dy}{y} = 13x \, dx$
integrate ...
$\displaystyle \ln|y| = \frac{13x^2}{2} + C_1$
$\displaystyle y = C_2e^{\frac{13x^2}{2}}$
$\displaystyle y(0) = 1$
$\displaystyle 1 = C_2e^0$
$\displaystyle C_2 = 1$
$\displaystyle y = e^{\frac{13x^2}{2}}$