4.45.17 $y^{⁗}(x)=a^{4}y(x)+x^3$

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

$$\left\{\{y(x)\to -\frac{x^3}{a^4}+c_2{e}^{-ax}+c_4{e}^{ax}+c_3\sin (ax)+c_1\cos (ax)\}\right\}$$

Maple ✓
cpu = 0.026 (sec), leaf count = 38

$$\{y\left(x\right)=-\frac{x^3}{a^4}+\mathit{\_}\mathit{C}\mathit{1}\cos \left(ax\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{ax}+\mathit{\_}\mathit{C}\mathit{3}\sin \left(ax\right)+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-ax}\}$$ 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)