ODE
\[ y(x)^2 y''(x)+y(x) y'(x)^2=a+b x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.497191 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[1][y][x]^2 + y[x]^2*Derivative[2][y][x] == a + b*x, y[x], x]
Maple ✓
cpu = 0.494 (sec), leaf count = 158
\[ \left \{ {\frac {a\ln \left ( bx+a \right ) }{b}}-\int ^{{\frac {y \left ( x \right ) }{bx+a}}}\!{\frac {{{\it \_g}}^{2}a\sqrt {3}}{6\,{{\it \_g}}^{3}{b}^{2}-6} \left ( 3\,a\tan \left ( {\it RootOf} \left ( 6\,{a}^{2}\int \!{\frac {{{\it \_g}}^{2}}{{{\it \_g}}^{3}{b}^{2}-1} \left ( -{\frac {b}{{{\it \_g}}^{3}{a}^{3}}} \right ) ^{2/3}}\,{\rm d}{\it \_g}-2\,{\it \_Z}\,\sqrt {3}+\ln \left ( {\frac { \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1}{3+2\,\sqrt {3}\tan \left ( {\it \_Z} \right ) + \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +6\,{\it \_C1} \right ) \right ) \sqrt [3]{-{\frac {b}{{{\it \_g}}^{3}{a}^{3}}}}+\sqrt {3}\sqrt [3]{-{\frac {b}{{{\it \_g}}^{3}{a}^{3}}}}a-2\,\sqrt {3}b \right ) }{d{\it \_g}}-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y'[x]^2 + y[x]^2*y''[x] == a + b*x,y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[1][y][x]^2 + y[x]^2*Derivative[2][y][x] == a + b*x, y[x], x]
Maple raw input
dsolve(y(x)^2*diff(diff(y(x),x),x)+y(x)*diff(y(x),x)^2 = b*x+a, y(x),'implicit')
Maple raw output
a*ln(b*x+a)/b-Intat(a*_g^2*(3*a*tan(RootOf(6*a^2*Int((-1/_g^3/a^3*b)^(2/3)/(_g^3*b^2-1)*_g^2,_g)-2*_Z*3^(1/2)+ln((tan(_Z)^2+1)/(3+2*3^(1/2)*tan(_Z)+tan(_Z)^2))+6*_C1))*(-1/_g^3/a^3*b)^(1/3)+3^(1/2)*(-1/_g^3/a^3*b)^(1/3)*a-2*3^(1/2)*b)*3^(1/2)/(6*_g^3*b^2-6),_g = y(x)/(b*x+a))-_C2 = 0