4.16.8 \(a x^2+b y(x)+y'(x)^2=0\)

ODE
\[ a x^2+b y(x)+y'(x)^2=0 \] 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

\[ \left \{ \int _{{\it \_b}}^{x}\!-{1\sqrt {-{{\it \_a}}^{2}a-by \relax (x ) } \left (\sqrt {-{{\it \_a}}^{2}a-by \relax (x ) }{\it \_a}-2\,y \relax (x ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\! \left (\sqrt {-a{x}^{2}-{\it \_f}\,b}x-2\,{\it \_f} \right ) ^{-1}-\int _{{\it \_b}}^{x}\!{1 \left (-{{\it \_f}\,b{\frac {1}{\sqrt {-{{\it \_a}}^{2}a-{\it \_f}\,b}}}}-2\,\sqrt {-{{\it \_a}}^{2}a-{\it \_f}\,b} \right ) \left (\sqrt {-{{\it \_a}}^{2}a-{\it \_f}\,b}{\it \_a}-2\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!-{1\sqrt {-{{\it \_a}}^{2}a-by \relax (x ) } \left (\sqrt {-{{\it \_a}}^{2}a-by \relax (x ) }{\it \_a}+2\,y \relax (x ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\!- \left (\sqrt {-a{x}^{2}-{\it \_f}\,b}x+2\,{\it \_f} \right ) ^{-1}-\int _{{\it \_b}}^{x}\!{1 \left ({{\it \_f}\,b{\frac {1}{\sqrt {-{{\it \_a}}^{2}a-{\it \_f}\,b}}}}+2\,\sqrt {-{{\it \_a}}^{2}a-{\it \_f}\,b} \right ) \left (\sqrt {-{{\it \_a}}^{2}a-{\it \_f}\,b}{\it \_a}+2\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \] 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