Question

Can someone me solving a linear differential equations, cos(x) (dy/dx) +ysen(x) =2xcos^(3)x
I have a problem with the integrating facytor u(x) =sec(x) but n get e^sec^(2)x

Answer 1

which of these methods did you try
separation of variable
Exact Equations
Bernoullis equation
variation of parameters
wronskian equation/determinant

you will definitely get a correct answer with Wronkian provided you are great at intergration

Answer 2

\[\mu(x)=\exp\left(\int\frac{\sin x}{\cos x}\right)\]

Answer 3

\[\int\frac{\sin x}{\cos x}dx\]\[u=\cos x\implies du=-\sin dx\]\[-\int\frac1udu=-\ln(\cos x)=\ln(\frac1{\cos x})=\ln\sec x\]\[e^{\ln\sec x}=\sec x\]try that ;)

Answer 4

he did.

Answer 5

Great it was like that, turning test!

Answer 6

welcome!
I always have to recheck integral tanxdx myself, a little confusing