4.44.44 $x^3{y}^{‴}(x)+x^2\log (x)y^{″}(x)+2x{y}^{\prime }(x)-y(x)=2x^3$

ODE
$$x^3{y}^{‴}(x)+x^2\log (x)y^{″}(x)+2x{y}^{\prime }(x)-y(x)=2x^3$$ ODE Classification

[[_3rd_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✗
cpu = 0.0143274 (sec), leaf count = 0 , could not solve

DSolve[-y[x] + 2*x*Derivative[1][y][x] + x^2*Log[x]*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 2*x^3, y[x], x]

Maple ✓
cpu = 0.365 (sec), leaf count = 141

$$\{y\left(x\right)=\frac{x^2}{3}{\mathrm{e}}^{-\frac{{(\ln \left(x\right))}^2}{2}}(-3\int ix\sqrt{2}{\mathrm{e}}^{1/2{(\ln \left(x\right))}^2}(x\mathit{E}\mathit{r}\mathit{f}\left(i/2\sqrt{2}(\ln \left(x\right)-2)\right){\mathrm{e}}^{1/2}-\mathit{E}\mathit{r}\mathit{f}\left(i/2\sqrt{2}(-1+\ln \left(x\right))\right){\mathrm{e}}^2)\sqrt{\pi }{\mathrm{e}}^{-1/2{(\ln \left(x\right))}^2}{\mathrm{e}}^{-5/2}\mathrm{d}x+(-\frac{3i}{2}{x}^2\sqrt{2}\sqrt{\pi }{\mathrm{e}}^{-\frac{1}{2}}+3\mathit{\_}\mathit{C}\mathit{2})\mathit{E}\mathit{r}\mathit{f}\left(\frac{i}{2}\sqrt{2}(-1+\ln \left(x\right))\right)+(i{x}^3\sqrt{2}\sqrt{\pi }{\mathrm{e}}^{-2}+3\mathit{\_}\mathit{C}\mathit{3})\mathit{E}\mathit{r}\mathit{f}\left(\frac{i}{2}\sqrt{2}(\ln \left(x\right)-2)\right)+3\mathit{\_}\mathit{C}\mathit{1})\}$$ Mathematica raw input

DSolve[-y[x] + 2*x*y'[x] + x^2*Log[x]*y''[x] + x^3*y'''[x] == 2*x^3,y[x],x]

Mathematica raw output

DSolve[-y[x] + 2*x*Derivative[1][y][x] + x^2*Log[x]*Derivative[2][y][x] + x^3*De
rivative[3][y][x] == 2*x^3, y[x], x]

Maple raw input

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+x^2*diff(diff(y(x),x),x)*ln(x)+2*x*diff(y(x),x)-y(x) = 2*x^3, y(x),'implicit')

Maple raw output

y(x) = 1/3*exp(-1/2*ln(x)^2)*(-3*Int(I*x*2^(1/2)*exp(1/2*ln(x)^2)*(x*erf(1/2*I*2
^(1/2)*(ln(x)-2))*exp(1/2)-erf(1/2*I*2^(1/2)*(-1+ln(x)))*exp(2))*Pi^(1/2)*exp(-1
/2*ln(x)^2)*exp(-5/2),x)+(-3/2*I*x^2*2^(1/2)*Pi^(1/2)*exp(-1/2)+3*_C2)*erf(1/2*I
*2^(1/2)*(-1+ln(x)))+(I*x^3*2^(1/2)*Pi^(1/2)*exp(-2)+3*_C3)*erf(1/2*I*2^(1/2)*(l
n(x)-2))+3*_C1)*x^2