Hi there,
I'm a newbie in differential equations and I'm having some difficulties with my assignment. Can anyone show me how to solve the following differential equations:

(a) y'
= cos 5x( e^sin 5x)
(b) xy' + xy = 1 -y, y(1) = 0

Really hope someone can help me solve the equations or at least show me hints on where to start to solve the questions. Thank you for reading my post. Many thanks advance

2. Originally Posted by b4byp4nd4
Hi there,
I'm a newbie in differential equations and I'm having some difficulties with my assignment. Can anyone show me how to solve the following differential equations:

(a) y'
= cos 5x( e^sin 5x)
just integrate both sides. (a substitution of $\displaystyle u = \sin 5x$ will help)
(b) xy' + xy = 1 -y, y(1) = 0

write as $\displaystyle xy' + (x + 1)y = 1$

$\displaystyle \Rightarrow y' + \frac {x + 1}xy = \frac 1x$

Now, complete using the integrating factor method

3. Thank you so much for the reply
I managed to solve the second question but still having difficulties with the first question. I ended up having y = integral of cos5x(e^sin5x)
Am I on the right path? What do I do next?

4. Originally Posted by b4byp4nd4
Thank you so much for the reply
I managed to solve the second question but still having difficulties with the first question. I ended up having y = integral of cos5x(e^sin5x)
Am I on the right path? What do I do next?
i told you, to do $\displaystyle \int \cos 5x e^{\sin 5x}~dx$ use a substitution of $\displaystyle u = \sin 5x$. you know how to do integration by substitution, right?

5. Ah.. now I see what I need to do. Thanks a lot for your help You Rock!!!