ODE
\[ y''(x)+2 \tan (x) y'(x)-y(x)=(x+1) \sec (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.495334 (sec), leaf count = 62
\[\left \{\left \{y(x)\to \frac {1}{2} \left (\sqrt {\sin ^2(x)}-\cos ^{-1}(\cos (x)) \cos (x)-\cos (x)+2 c_2 \cos (x)+2 c_1 \sqrt {\sin ^2(x)}-2 c_2 \sqrt {\sin ^2(x)} \sin ^{-1}(\cos (x))\right )\right \}\right \}\]
Maple ✓
cpu = 4.453 (sec), leaf count = 117
\[\left [y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\left (\ln \left (\sin \left (x \right )+i \cos \left (x \right )\right ) \sin \left (x \right )-i \cos \left (x \right )\right ) \textit {\_C1} +\frac {2 i \left (\int \frac {\left (\ln \left (\sin \left (x \right )+i \cos \left (x \right )\right ) \sin \left (x \right )-i \cos \left (x \right )\right ) \left (x +1\right )}{\cos \left (x \right )^{3}}d x \right ) \sin \left (x \right ) \left (\cos ^{2}\left (x \right )\right )+\left (-i \left (\cos ^{3}\left (x \right )\right )+i \cos \left (x \right )-i \sin \left (x \right ) \left (x +1\right )\right ) \ln \left (\sin \left (x \right )+i \cos \left (x \right )\right )-\cos \left (x \right ) \left (-\cos \left (x \right ) \sin \left (x \right )+x +1\right )}{2 \cos \left (x \right )^{2}}\right ]\] Mathematica raw input
DSolve[-y[x] + 2*Tan[x]*y'[x] + y''[x] == (1 + x)*Sec[x],y[x],x]
Mathematica raw output
{{y[x] -> (-Cos[x] - ArcCos[Cos[x]]*Cos[x] + 2*C[2]*Cos[x] + Sqrt[Sin[x]^2] + 2*C[1]*Sqrt[Sin[x]^2] - 2*ArcSin[Cos[x]]*C[2]*Sqrt[Sin[x]^2])/2}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)*tan(x)-y(x) = sec(x)*(x+1), y(x))
Maple raw output
[y(x) = sin(x)*_C2+(ln(sin(x)+I*cos(x))*sin(x)-I*cos(x))*_C1+1/2*(2*I*Int((ln(sin(x)+I*cos(x))*sin(x)-I*cos(x))/cos(x)^3*(x+1),x)*sin(x)*cos(x)^2+(-I*cos(x)^3+I*cos(x)-I*sin(x)*(x+1))*ln(sin(x)+I*cos(x))-cos(x)*(-cos(x)*sin(x)+x+1))/cos(x)^2]