00:01
Okay, so in this problem we want to solve a differential equation, the y over dx equals to x over y times sine of x.
00:10
This is an autonomous differential equation.
00:12
That means we can rewrite this differential equation as y times the y equals to x times sine of x times d x and we can integrate both sides.
00:26
So for the left side, we have one half, have y square plus a constant c1.
00:33
For the right hand side, we need to use integration by part.
00:37
That u equals to x, u equals to dx, and the dv equals to sine of x, dx, and the v equals to minus cosine of x.
00:49
So this is the integration by part we use.
01:04
So the right hand side equals to minus x cosine of x plus integral cosine of x d x, which is minus x, cosine, x, plus sine of x plus a constant c2...