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

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

[[_homogeneous, `class G`]]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 600. (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.182 (sec), leaf count = 394

\[ \left \{ \int _{{\it \_b}}^{x}\!{1 \left (-{\it \_a}\,a-\sqrt {-4\,cy \relax (x ) + \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}} \right ) \left ({{\it \_a}}^{2}a+{\it \_a}\,\sqrt {-4\,cy \relax (x ) + \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}}+4\,y \relax (x ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\!-2\, \left (a{x}^{2}+x\sqrt { \left ({a}^{2}-4\,b \right ) {x}^{2}-4\,{\it \_f}\,c}+4\,{\it \_f} \right ) ^{-1}-\int _{{\it \_b}}^{x}\!{1 \left (8\,{\frac {{\it \_f}\,c}{\sqrt { \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c}}}+4\,{\it \_a}\,a+4\,\sqrt { \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c} \right ) \left ({{\it \_a}}^{2}a+{\it \_a}\,\sqrt { \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c}+4\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{1 \left (-{\it \_a}\,a+\sqrt {-4\,cy \relax (x ) + \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}} \right ) \left ({{\it \_a}}^{2}a-{\it \_a}\,\sqrt {-4\,cy \relax (x ) + \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}}+4\,y \relax (x ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\!2\, \left (-a{x}^{2}+x\sqrt { \left ({a}^{2}-4\,b \right ) {x}^{2}-4\,{\it \_f}\,c}-4\,{\it \_f} \right ) ^{-1}-\int _{{\it \_b}}^{x}\!{1 \left (-8\,{\frac {{\it \_f}\,c}{\sqrt { \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c}}}+4\,{\it \_a}\,a-4\,\sqrt { \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c} \right ) \left ({{\it \_a}}^{2}a-{\it \_a}\,\sqrt { \left ({a}^{2}-4\,b \right ) {{\it \_a}}^{2}-4\,{\it \_f}\,c}+4\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

Int((-_a*a-(-4*c*y(x)+(a^2-4*b)*_a^2)^(1/2))/(_a^2*a+_a*(-4*c*y(x)+(a^2-4*b)*_a^
2)^(1/2)+4*y(x)),_a = _b .. x)+Intat(-2/(a*x^2+x*((a^2-4*b)*x^2-4*_f*c)^(1/2)+4*
_f)-Int((8*c*_f/((a^2-4*b)*_a^2-4*_f*c)^(1/2)+4*_a*a+4*((a^2-4*b)*_a^2-4*_f*c)^(
1/2))/(_a^2*a+_a*((a^2-4*b)*_a^2-4*_f*c)^(1/2)+4*_f)^2,_a = _b .. x),_f = y(x))+
_C1 = 0, Int((-_a*a+(-4*c*y(x)+(a^2-4*b)*_a^2)^(1/2))/(_a^2*a-_a*(-4*c*y(x)+(a^2
-4*b)*_a^2)^(1/2)+4*y(x)),_a = _b .. x)+Intat(2/(-a*x^2+x*((a^2-4*b)*x^2-4*_f*c)
^(1/2)-4*_f)-Int((-8*c*_f/((a^2-4*b)*_a^2-4*_f*c)^(1/2)+4*_a*a-4*((a^2-4*b)*_a^2
-4*_f*c)^(1/2))/(_a^2*a-_a*((a^2-4*b)*_a^2-4*_f*c)^(1/2)+4*_f)^2,_a = _b .. x),_
f = y(x))+_C1 = 0