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 = 0.03871 (sec), leaf count = 48
\[\left \{\left \{y(x)\to \frac {1}{72} e^{-x} \left (-9 e^{2 x} \left (-8 c_2+2 x+1\right )+72 c_3 e^{3 x}+72 c_1-6 x-5\right )\right \}\right \}\]
Maple ✓
cpu = 0.06 (sec), leaf count = 82
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -6\,x+3\,\cosh \left ( 2\,x \right ) +3\,\sinh \left ( 2\,x \right ) +72\,{\it \_C2}+3 \right ) {{\rm e}^{-x}}}{72}}+{\frac { \left ( 4\,\cosh \left ( 3\,x \right ) -4\,\sinh \left ( 3\,x \right ) +72\,{\it \_C3}-12\,\cosh \left ( x \right ) +12\,\sinh \left ( x \right ) \right ) {{\rm e}^{2\,x}}}{72}}-{\frac {{{\rm e}^{x}}}{4} \left ( x+{\frac {\cosh \left ( 2\,x \right ) }{2}}-{\frac {\sinh \left ( 2\,x \right ) }{2}}-4\,{\it \_C1} \right ) } \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/72*(-6*x+3*cosh(2*x)+3*sinh(2*x)+72*_C2+3)*exp(-x)+1/72*(4*cosh(3*x)-4*sinh(3*x)+72*_C3-12*cosh(x)+12*sinh(x))*exp(2*x)-1/4*(x+1/2*cosh(2*x)-1/2*sinh(2*x)-4*_C1)*exp(x)