4.45.4 $x^4{y}^{‴}(x)+2x^3{y}^{″}(x)-x^2{y}^{\prime }(x)+xy(x)=1$

ODE
$$x^4{y}^{‴}(x)+2x^3{y}^{″}(x)-x^2{y}^{\prime }(x)+xy(x)=1$$ ODE Classification

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0174024 (sec), leaf count = 33

$$\left\{\{y(x)\to \frac{c_1}{x}+c_{2}x+c_{3}x\log (x)+\frac{\log (x)+1}{4x}\}\right\}$$

Maple ✓
cpu = 0.021 (sec), leaf count = 30

$$\{y\left(x\right)=\frac{4\mathit{\_}\mathit{C}\mathit{3}{x}^2\ln \left(x\right)+4\mathit{\_}\mathit{C}\mathit{1}{x}^2+\ln \left(x\right)+4\mathit{\_}\mathit{C}\mathit{2}+1}{4x}\}$$ Mathematica raw input

DSolve[x*y[x] - x^2*y'[x] + 2*x^3*y''[x] + x^4*y'''[x] == 1,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/x + x*C[2] + x*C[3]*Log[x] + (1 + Log[x])/(4*x)}}

Maple raw input

dsolve(x^4*diff(diff(diff(y(x),x),x),x)+2*x^3*diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x) = 1, y(x),'implicit')

Maple raw output

y(x) = 1/4*(4*_C3*x^2*ln(x)+4*_C1*x^2+ln(x)+4*_C2+1)/x