4.29.2 $(1-x)y^{″}(x)+x{y}^{\prime }(x)-y(x)=(1-x{)}^2$

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

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0233116 (sec), leaf count = 22

$$\left\{\{y(x)\to -c_{2}x+c_1{e}^x+x^2+x+1\}\right\}$$

Maple ✓
cpu = 0.017 (sec), leaf count = 16

$$\{y\left(x\right)=x\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^x\mathit{\_}\mathit{C}\mathit{1}+x^2+1\}$$ Mathematica raw input

DSolve[-y[x] + x*y'[x] + (1 - x)*y''[x] == (1 - x)^2,y[x],x]

Mathematica raw output

{{y[x] -> 1 + x + x^2 + E^x*C[1] - x*C[2]}}

Maple raw input

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

Maple raw output

y(x) = x*_C2+exp(x)*_C1+x^2+1