4.45.36 $-2y^{‴}(x)+y^{⁗}(x)+y(x{)}^2=0$

ODE
$$-2y^{‴}(x)+y^{⁗}(x)+y(x{)}^2=0$$ ODE Classification

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✗
cpu = 0.024828 (sec), leaf count = 0 , could not solve

DSolve[y[x]^2 - 2*Derivative[3][y][x] + Derivative[4][y][x] == 0, y[x], x]

Maple ✓
cpu = 0.904 (sec), leaf count = 91

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{{\mathrm{d}}^3}{\mathrm{d}{\mathit{\_}\mathit{a}}^3}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+4(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-1/2){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\frac{{\mathrm{d}}^2}{\mathrm{d}{\mathit{\_}\mathit{a}}^2}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-2{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+{\mathit{\_}\mathit{a}}^2=0\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\},\{x=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$ Mathematica raw input

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

Mathematica raw output

DSolve[y[x]^2 - 2*Derivative[3][y][x] + Derivative[4][y][x] == 0, y[x], x]

Maple raw input

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

Maple raw output

y(x) = ODESolStruc(_a,[{diff(diff(diff(_b(_a),_a),_a),_a)*_b(_a)^3+4*(diff(_b(_a
),_a)-1/2)*_b(_a)^2*diff(diff(_b(_a),_a),_a)+diff(_b(_a),_a)^3*_b(_a)-2*diff(_b(
_a),_a)^2*_b(_a)+_a^2 = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a
),_a)+_C1, y(x) = _a}])