ODE
\[ y''(x)+4 y'(x)+5 y(x)=\sin (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0157289 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {1}{8} \left (8 c_1 e^{-2 x} \sin (x)+8 c_2 e^{-2 x} \cos (x)+\sin (x)-\cos (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-2\,x}}\sin \left ( x \right ) {\it \_C2}+{{\rm e}^{-2\,x}}\cos \left ( x \right ) {\it \_C1}-{\frac {\cos \left ( x \right ) }{8}}+{\frac {\sin \left ( x \right ) }{8}} \right \} \] Mathematica raw input
DSolve[5*y[x] + 4*y'[x] + y''[x] == Sin[x],y[x],x]
Mathematica raw output
{{y[x] -> (-Cos[x] + (8*C[2]*Cos[x])/E^(2*x) + Sin[x] + (8*C[1]*Sin[x])/E^(2*x))/8}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+4*diff(y(x),x)+5*y(x) = sin(x), y(x),'implicit')
Maple raw output
y(x) = exp(-2*x)*sin(x)*_C2+exp(-2*x)*cos(x)*_C1-1/8*cos(x)+1/8*sin(x)