How to solve simple trig function differential equation? Probably the title is too general. Well, the following is just a question a few people asked me for help. I am posting this question's solution here so it may help you. if you run into similar problems.

Question: Solve y''(x)=sin(x) if y(0)=0 and y'(0)=7.

Basically this problem involves two steps. In order to find y(x) we need to find y'(x) first by setting up an integral. After that, we can find y(x) through y'(x) by setting up another integral and do the evaluations.

Solution: