ODE
\[ y''(x)+2 y'(x)+5 y(x)=8 \sinh (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0293027 (sec), leaf count = 37
\[\left \{\left \{y(x)\to \frac {1}{2} e^{-x} \left (2 c_1 \sin (2 x)+2 c_2 \cos (2 x)+e^{2 x}-2\right )\right \}\right \}\]
Maple ✓
cpu = 0.091 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac { \left ( \left ( 2\,{\it \_C1}-2 \right ) \cos \left ( 2\,x \right ) +2\,{\it \_C2}\,\sin \left ( 2\,x \right ) -2 \right ) {{\rm e}^{-x}}}{2}}+{\frac {{{\rm e}^{x}}}{2}} \right \} \] Mathematica raw input
DSolve[5*y[x] + 2*y'[x] + y''[x] == 8*Sinh[x],y[x],x]
Mathematica raw output
{{y[x] -> (-2 + E^(2*x) + 2*C[2]*Cos[2*x] + 2*C[1]*Sin[2*x])/(2*E^x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)+5*y(x) = 8*sinh(x), y(x),'implicit')
Maple raw output
y(x) = 1/2*((2*_C1-2)*cos(2*x)+2*_C2*sin(2*x)-2)*exp(-x)+1/2*exp(x)