ODE
\[ y''''(x)=a^4 y(x)+x^3 \] ODE Classification
[[_high_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00844123 (sec), leaf count = 45
\[\left \{\left \{y(x)\to -\frac {x^3}{a^4}+c_2 e^{-a x}+c_4 e^{a x}+c_3 \sin (a x)+c_1 \cos (a x)\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 38
\[ \left \{ y \left ( x \right ) =-{\frac {{x}^{3}}{{a}^{4}}}+{\it \_C1}\,\cos \left ( ax \right ) +{\it \_C2}\,{{\rm e}^{ax}}+{\it \_C3}\,\sin \left ( ax \right ) +{\it \_C4}\,{{\rm e}^{-ax}} \right \} \] Mathematica raw input
DSolve[y''''[x] == x^3 + a^4*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(x^3/a^4) + C[2]/E^(a*x) + E^(a*x)*C[4] + C[1]*Cos[a*x] + C[3]*Sin[a*x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x) = x^3+a^4*y(x), y(x),'implicit')
Maple raw output
y(x) = -1/a^4*x^3+_C1*cos(a*x)+_C2*exp(a*x)+_C3*sin(a*x)+_C4*exp(-a*x)