# Thread: 1.3.4 verify that the function is a solution of the DE.

1. ## 1.3.4 verify that the function is a solution of the DE.

ok finally number 14
I assume s means seconds. and we have y, t and s is in this

2. ## Re: 1.3.4 verify that the function is a solution of the DE.

Originally Posted by bigwave

ok finally number 14
I assume s means seconds. and we have y, t and s is in this
Not likely. s and t are more likely just throw away variables. (I've seen them typically used in Laplace transform problems.)

The difficulty here is taking the derivative of the integral? Just break it into pieces, as always.
$\displaystyle y = e^{t^2} \int _0^t e^{-s^2}~ds + e^{t^2}$

$\displaystyle y' = \dfrac{d}{dt} (e^{t^2}) \cdot \int _0^t e^{-s^2}~ds + e^{t^2} \cdot \dfrac{d}{dt} \left ( \int _0^t e^{-s^2}~ds \right ) + \dfrac{d}{dt} (e^{t^2} )$

Can you do the derivatives?

-Dan