ODE
\[ y''(x)+y(x)=\tan ^2(x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.22364 (sec), leaf count = 50
\[\left \{\left \{y(x)\to c_1 \cos (x)+\sin (x) \left (-\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_2\right )-2\right \}\right \}\]
Maple ✓
cpu = 0.498 (sec), leaf count = 27
\[\left [y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\textit {\_C1} \cos \left (x \right )-2+\sin \left (x \right ) \ln \left (\frac {1+\sin \left (x \right )}{\cos \left (x \right )}\right )\right ]\] Mathematica raw input
DSolve[y[x] + y''[x] == Tan[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -2 + C[1]*Cos[x] + (C[2] - Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]])*Sin[x]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x) = tan(x)^2, y(x))
Maple raw output
[y(x) = sin(x)*_C2+_C1*cos(x)-2+sin(x)*ln((1+sin(x))/cos(x))]