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 = 20.5394 (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 = 3.888 (sec), leaf count = 157
\[\left [\frac {a \ln \left (b x +a \right )}{b}-\frac {\sqrt {3}\, \left (\int _{}^{\frac {y \left (x \right )}{b x +a}}\frac {a \,\textit {\_g}^{2} \left (\left (-\frac {b}{\textit {\_g}^{3} a^{3}}\right )^{\frac {1}{3}} \sqrt {3}\, a +3 a \left (-\frac {b}{\textit {\_g}^{3} a^{3}}\right )^{\frac {1}{3}} \tan \left (\RootOf \left (6 a^{2} \left (\int \frac {\left (-\frac {b}{\textit {\_g}^{3} a^{3}}\right )^{\frac {2}{3}} \textit {\_g}^{2}}{\textit {\_g}^{3} b^{2}-1}d \textit {\_g} \right )-2 \sqrt {3}\, \textit {\_Z} +\ln \left (\frac {\tan ^{2}\left (\textit {\_Z} \right )+1}{\tan ^{2}\left (\textit {\_Z} \right )+2 \sqrt {3}\, \tan \left (\textit {\_Z} \right )+3}\right )+6 \textit {\_C1} \right )\right )-2 \sqrt {3}\, b \right )}{\textit {\_g}^{3} b^{2}-1}d \textit {\_g} \right )}{6}-\textit {\_C2} = 0\right ]\] 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))
Maple raw output
[a*ln(b*x+a)/b-1/6*3^(1/2)*Intat(a*_g^2*((-1/_g^3/a^3*b)^(1/3)*3^(1/2)*a+3*a*(-1/_g^3/a^3*b)^(1/3)*tan(RootOf(6*a^2*Int((-1/_g^3/a^3*b)^(2/3)/(_g^3*b^2-1)*_g^2,_g)-2*3^(1/2)*_Z+ln((tan(_Z)^2+1)/(tan(_Z)^2+2*3^(1/2)*tan(_Z)+3))+6*_C1))-2*3^(1/2)*b)/(_g^3*b^2-1),_g = y(x)/(b*x+a))-_C2 = 0]