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 = 0.0475135 (sec), leaf count = 47
\[\left \{\left \{y(x)\to \frac {1}{64} e^{-3 x} \left (-8 e^{2 x} \left (x-8 c_2\right )+e^{4 x} \left (64 c_3+4 x-3\right )+64 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.039 (sec), leaf count = 82
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 2\,\sinh \left ( 2\,x \right ) +\sinh \left ( 4\,x \right ) +64\,{\it \_C2}+2\,\cosh \left ( 2\,x \right ) +\cosh \left ( 4\,x \right ) \right ) {{\rm e}^{-3\,x}}}{64}}+{\frac { \left ( -8\,x-4\,\sinh \left ( 2\,x \right ) +64\,{\it \_C3}-4\,\cosh \left ( 2\,x \right ) -4 \right ) {{\rm e}^{-x}}}{64}}+{\frac {{{\rm e}^{x}}}{16} \left ( x+{\frac {\sinh \left ( 2\,x \right ) }{2}}+16\,{\it \_C1}-{\frac {\cosh \left ( 2\,x \right ) }{2}} \right ) } \right \} \] Mathematica raw input
DSolve[-3*y[x] - y'[x] + 3*y''[x] + y'''[x] == Cosh[x],y[x],x]
Mathematica raw output
{{y[x] -> (64*C[1] - 8*E^(2*x)*(x - 8*C[2]) + E^(4*x)*(-3 + 4*x + 64*C[3]))/(64*E^(3*x))}}
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),'implicit')
Maple raw output
y(x) = 1/64*(2*sinh(2*x)+sinh(4*x)+64*_C2+2*cosh(2*x)+cosh(4*x))*exp(-3*x)+1/64*(-8*x-4*sinh(2*x)+64*_C3-4*cosh(2*x)-4)*exp(-x)+1/16*(x+1/2*sinh(2*x)+16*_C1-1/2*cosh(2*x))*exp(x)