Question

2nd order ODE
Variation of Parameters

Answer 1

Solve the following differential equation.
\(y''+4y=tan~2x\)

Answer 2

\(a=1~~~and~~~f(x)=tan~2x\)

Answer 3

\(m^2+4=0\)

\(m^2=-4\)

\(m=\pm2i\)

Answer 4

\(y_h(x)=Acos2x+Bsin2x\)

\(y_1(x)=cos2x~~~,~~~y_2(x)=sin2x\)

Answer 5

\(w=cos2x(2cos2x)-sin2x(-2sin2x)\)

\(w=2cos^2x-2sin^22x\)

Answer 6

yeah you are correct so far

Answer 7

I was trying to find \(u(x)\) and \(v(x)\) but it looks weird a bit