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

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

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica ✗
cpu = 101.668 (sec), leaf count = 0 , could not solve

DSolve[b*y[x] + a*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]

Maple ✓
cpu = 0.168 (sec), leaf count = 79

\[ \left \{ \int ^{y \left ( x \right ) }\!-2\,{\frac {a}{\sqrt {4\,{{\rm e}^{-2\,{\it \_a}\,a}}{\it \_C1}\,{a}^{2}-4\,b{\it \_a}\,a+2\,b}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!2\,{\frac {a}{\sqrt {4\,{{\rm e}^{-2\,{\it \_a}\,a}}{\it \_C1}\,{a}^{2}-4\,b{\it \_a}\,a+2\,b}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

DSolve[b*y[x] + a*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]

Maple raw input

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

Maple raw output

Intat(-2/(4*exp(-2*_a*a)*_C1*a^2-4*b*_a*a+2*b)^(1/2)*a,_a = y(x))-x-_C2 = 0, Int
at(2/(4*exp(-2*_a*a)*_C1*a^2-4*b*_a*a+2*b)^(1/2)*a,_a = y(x))-x-_C2 = 0