# differential equation verification

• Feb 4th 2009, 03:09 PM
crafty
differential equation verification
(dy/dt) + y = cos(e^t) i got the integrating factor as e^t and the answer i got is y = (1/(e^t))*(sin (e^t)) + C is this correct???
• Feb 4th 2009, 03:14 PM
Jester
Quote:

Originally Posted by crafty
(dy/dt) + y = cos(e^t) i got the integrating factor as e^t and the answer i got is y = (1/(e^t))*(sin (e^t)) + C is this correct???

Very close, when you integrate, you get

$\displaystyle e^t y = \sin e^t + c$

Dividing by $\displaystyle e^t$ you must keep the c where it is,

$\displaystyle y = \frac{\sin e^t + c}{e^t}$ a little different from your answer.
• Feb 4th 2009, 03:22 PM
crafty
but isnt c just an arbitrary constant and assuming my c outside is a different constant would it still be correct or is there something special about this case, if there is can you explain why ... thanks in advance
• Feb 4th 2009, 03:27 PM
Jester
Quote:

Originally Posted by crafty
but isnt c just an arbitrary constant and assuming my c outside is a different constant would it still be correct or is there something special about this case, if there is can you explain why ... thanks in advance

Your right c is an arbitrary constant but when multiplied by a function of t then it will change with respect to t (it's no longer fixed). This is really seen if you were given an initial condition were the value of c would be set.
• Feb 4th 2009, 03:38 PM
crafty
oh right i get it now and can you please reply to my other thread called its called "how do is solve this differential eqn???" ive been waiting a while for that one and i still don't get it