4.42.14 $y^{″}(x{)}^2-x{y}^{″}(x)+y^{\prime }(x)=0$

ODE
$$y^{″}(x{)}^2-x{y}^{″}(x)+y^{\prime }(x)=0$$ ODE Classification

[[_2nd_order, _missing_y]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00793341 (sec), leaf count = 21

$$\left\{\{y(x)\to \frac{1}{2}{c}_{1}x(x-2c_1)+c_2\}\right\}$$

Maple ✓
cpu = 0.092 (sec), leaf count = 28

$$\{y\left(x\right)=\frac{x^3}{12}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^2}{2}-{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+\mathit{\_}\mathit{C}\mathit{2}\}$$ Mathematica raw input

DSolve[y'[x] - x*y''[x] + y''[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(y(x),x),x)^2-x*diff(diff(y(x),x),x)+diff(y(x),x) = 0, y(x),'implicit')

Maple raw output

y(x) = 1/12*x^3+_C1, y(x) = 1/2*_C1*x^2-_C1^2*x+_C2