00:01
In this problem we are going to solve the following differential equation.
00:07
1 plus y squared sine 2x dx minus 2y cosine x squared dy equal to 0.
00:21
I am going to call this function m and this function n.
00:27
So let us try the following.
00:30
Partial m over partial y is given by 2y sine 2x and partial n over partial x is minus 2y 2 cosine x minus sine x.
00:50
So this is equal to 2y sine 2x.
00:55
Therefore we see that partial m over partial y is equal to partial n over partial x.
01:03
Therefore this differential equation is exact.
01:07
This means there exists some function f of x and the solution is f of x equal to some constant c.
01:18
So we are going to obtain an implicit solution for this differential equation.
01:24
And this f is such that partial f over partial x is m and partial f over partial y is n.
01:35
Ok let's start with the x derivative...