Solve initial value problem using sep. of variables
y(prime)=cos^2(x) y(0)=pi/4
I ended up using integration by parts and got to here:
y=cosx * sinx - x + C
and C= pi/4
but the book says the answer is:
y=.5(x+.5sin(2x))+pi/4
what did I do wrong?
Are you trying to do separation of variables or integration by parts? They're two different methods.
You only use separation of variables if you have a Separable linear DE, which you don't, so I guess you're trying to do integration by parts...
Integration by parts is as follows...
.
So if you're integrating , then and . So what are and ?
In this case you should end up with ... not fun to work with as it's just as bad as . Just use the trig identity.