ODE
\[ y'''(x)+3 y''(x)-y'(x)-3 y(x)=\cosh (x) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.185756 (sec), leaf count = 43
\[\left \{\left \{y(x)\to c_1 e^{-3 x}+e^{-x} \left (-\frac {x}{8}+c_2\right )+e^x \left (\frac {x}{16}-\frac {3}{64}+c_3\right )\right \}\right \}\]
Maple ✓
cpu = 0.486 (sec), leaf count = 99
\[\left [y \left (x \right ) = \frac {x \,{\mathrm e}^{x}}{16}+\frac {{\mathrm e}^{x} \sinh \left (2 x \right )}{32}-\frac {{\mathrm e}^{x} \cosh \left (2 x \right )}{32}+\frac {{\mathrm e}^{-3 x} \sinh \left (2 x \right )}{32}+\frac {{\mathrm e}^{-3 x} \sinh \left (4 x \right )}{64}+\frac {{\mathrm e}^{-3 x} \cosh \left (2 x \right )}{32}+\frac {{\mathrm e}^{-3 x} \cosh \left (4 x \right )}{64}-\frac {{\mathrm e}^{x}}{16}-\frac {{\mathrm e}^{-x}}{16}-\frac {x \,{\mathrm e}^{-x}}{8}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-3 x}+\textit {\_C3} \,{\mathrm e}^{-x}\right ]\] Mathematica raw input
DSolve[-3*y[x] - y'[x] + 3*y''[x] + y'''[x] == Cosh[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^(3*x) + (-1/8*x + C[2])/E^x + E^x*(-3/64 + x/16 + C[3])}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-diff(y(x),x)-3*y(x) = cosh(x), y(x))
Maple raw output
[y(x) = 1/16*x*exp(x)+1/32*exp(x)*sinh(2*x)-1/32*exp(x)*cosh(2*x)+1/32*exp(-3*x)*sinh(2*x)+1/64*exp(-3*x)*sinh(4*x)+1/32*exp(-3*x)*cosh(2*x)+1/64*exp(-3*x)*cosh(4*x)-1/16*exp(x)-1/16*exp(-x)-1/8*x*exp(-x)+_C1*exp(x)+_C2*exp(-3*x)+_C3*exp(-x)]