ODE
\[ y'''(x)-2 y''(x)-y'(x)+2 y(x)=\sinh (x) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.191766 (sec), leaf count = 48
\[\left \{\left \{y(x)\to \frac {1}{72} e^{-x} \left (-6 x-9 e^{2 x} (2 x+1-8 c_2)+72 c_3 e^{3 x}-5+72 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.515 (sec), leaf count = 63
\[\left [y \left (x \right ) = -\frac {x \,{\mathrm e}^{x}}{4}-\frac {{\mathrm e}^{-x}}{12}-\frac {{\mathrm e}^{x}}{8}-\frac {x \,{\mathrm e}^{-x}}{12}-\frac {{\mathrm e}^{2 x} \sinh \left (3 x \right )}{18}+\frac {{\mathrm e}^{2 x} \cosh \left (3 x \right )}{18}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-x}+\textit {\_C3} \,{\mathrm e}^{2 x}\right ]\] Mathematica raw input
DSolve[2*y[x] - y'[x] - 2*y''[x] + y'''[x] == Sinh[x],y[x],x]
Mathematica raw output
{{y[x] -> (-5 - 6*x + 72*C[1] - 9*E^(2*x)*(1 + 2*x - 8*C[2]) + 72*E^(3*x)*C[3])/(72*E^x)}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-diff(y(x),x)+2*y(x) = sinh(x), y(x))
Maple raw output
[y(x) = -1/4*x*exp(x)-1/12*exp(-x)-1/8*exp(x)-1/12*x*exp(-x)-1/18*exp(2*x)*sinh(3*x)+1/18*exp(2*x)*cosh(3*x)+_C1*exp(x)+_C2*exp(-x)+_C3*exp(2*x)]