ODE
\[ y''''(x)+2 y''(x)+y(x)=24 x \sin (x) \] ODE Classification
[[_high_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.117397 (sec), leaf count = 46
\[\left \{\left \{y(x)\to \frac {1}{2} \left (\left (2 c_4+9\right ) x+2 c_3-2 x^3\right ) \sin (x)+\left (c_2 x+c_1-3 x^2+3\right ) \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.151 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 2\,{\it \_C3}\,x-6\,{x}^{2}+2\,{\it \_C1}+3 \right ) \cos \left ( x \right ) }{2}}- \left ( {x}^{3}+ \left ( -{\it \_C4}-3 \right ) x-{\it \_C2} \right ) \sin \left ( x \right ) \right \} \] Mathematica raw input
DSolve[y[x] + 2*y''[x] + y''''[x] == 24*x*Sin[x],y[x],x]
Mathematica raw output
{{y[x] -> (3 - 3*x^2 + C[1] + x*C[2])*Cos[x] + ((-2*x^3 + 2*C[3] + x*(9 + 2*C[4]))*Sin[x])/2}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(y(x),x),x)+y(x) = 24*x*sin(x), y(x),'implicit')
Maple raw output
y(x) = 1/2*(2*_C3*x-6*x^2+2*_C1+3)*cos(x)-(x^3+(-_C4-3)*x-_C2)*sin(x)