4.16.8 $a{x}^2+by(x)+y^{\prime }(x{)}^2=0$

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

[[_homogeneous, `class G`]]

Book solution method
No Missing Variables ODE, Solve for $y$

Mathematica ✗
cpu = 599.992 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.249 (sec), leaf count = 280

$$\{{\int }_{\mathit{\_}\mathit{b}}^x-1\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-by\left(x\right)}{(\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-by\left(x\right)}\mathit{\_}\mathit{a}-2y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}{(\sqrt{-a{x}^2-\mathit{\_}\mathit{f}b}x-2\mathit{\_}\mathit{f})}^{-1}-{\int }_{\mathit{\_}\mathit{b}}^{x}1(-\mathit{\_}\mathit{f}b\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-\mathit{\_}\mathit{f}b}}-2\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-\mathit{\_}\mathit{f}b}){(\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-\mathit{\_}\mathit{f}b}\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{f})}^{-2}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^x-1\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-by\left(x\right)}{(\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-by\left(x\right)}\mathit{\_}\mathit{a}+2y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-{(\sqrt{-a{x}^2-\mathit{\_}\mathit{f}b}x+2\mathit{\_}\mathit{f})}^{-1}-{\int }_{\mathit{\_}\mathit{b}}^{x}1(\mathit{\_}\mathit{f}b\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-\mathit{\_}\mathit{f}b}}+2\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-\mathit{\_}\mathit{f}b}){(\sqrt{-{\mathit{\_}\mathit{a}}^{2}a-\mathit{\_}\mathit{f}b}\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{f})}^{-2}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

Int(-1/((-_a^2*a-b*y(x))^(1/2)*_a-2*y(x))*(-_a^2*a-b*y(x))^(1/2),_a = _b .. x)+I
ntat(1/((-a*x^2-_f*b)^(1/2)*x-2*_f)-Int((-b*_f/(-_a^2*a-_f*b)^(1/2)-2*(-_a^2*a-_
f*b)^(1/2))/((-_a^2*a-_f*b)^(1/2)*_a-2*_f)^2,_a = _b .. x),_f = y(x))+_C1 = 0, I
nt(-1/((-_a^2*a-b*y(x))^(1/2)*_a+2*y(x))*(-_a^2*a-b*y(x))^(1/2),_a = _b .. x)+In
tat(-1/((-a*x^2-_f*b)^(1/2)*x+2*_f)-Int((b*_f/(-_a^2*a-_f*b)^(1/2)+2*(-_a^2*a-_f
*b)^(1/2))/((-_a^2*a-_f*b)^(1/2)*_a+2*_f)^2,_a = _b .. x),_f = y(x))+_C1 = 0