# Thread:

1. ## 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???

2. 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

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

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

$y = \frac{\sin e^t + c}{e^t}$ a little different from your answer.

3. 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

4. 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.

5. 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
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