ODE
\[ a x^2 y'(x)^2+b x y(x) y'(x)+c y(x)^2+x^2 y(x) y''(x) \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.159781 (sec), leaf count = 0 , could not solve
DSolve[c*y[x]^2 + b*x*y[x]*Derivative[1][y][x] + a*x^2*Derivative[1][y][x]^2 + x^2*y[x]*Derivative[2][y][x], y[x], x]
Maple ✓
cpu = 0.739 (sec), leaf count = 127
\[\left [y \left (x \right ) = x^{-\frac {\sqrt {-4 a c +b^{2}-2 b -4 c +1}}{2 \left (1+a \right )}} x^{-\frac {b}{2 \left (1+a \right )}} x^{\frac {1}{2+2 a}} \left (\frac {-4 a c +b^{2}-2 b -4 c +1}{\left (x^{\sqrt {-4 a c +b^{2}-2 b -4 c +1}} \textit {\_C1} a +x^{\sqrt {-4 a c +b^{2}-2 b -4 c +1}} \textit {\_C1} -\textit {\_C2} a -\textit {\_C2} \right )^{2}}\right )^{-\frac {1}{2 \left (1+a \right )}}\right ]\] Mathematica raw input
DSolve[c*y[x]^2 + b*x*y[x]*y'[x] + a*x^2*y'[x]^2 + x^2*y[x]*y''[x],y[x],x]
Mathematica raw output
DSolve[c*y[x]^2 + b*x*y[x]*Derivative[1][y][x] + a*x^2*Derivative[1][y][x]^2 + x^2*y[x]*Derivative[2][y][x], y[x], x]
Maple raw input
dsolve(x^2*y(x)*diff(diff(y(x),x),x)+a*x^2*diff(y(x),x)^2+b*x*y(x)*diff(y(x),x)+c*y(x)^2, y(x))
Maple raw output
[y(x) = x^(-1/2/(1+a)*(-4*a*c+b^2-2*b-4*c+1)^(1/2))*x^(-1/2/(1+a)*b)*x^(1/2/(1+a))*((-4*a*c+b^2-2*b-4*c+1)/(x^((-4*a*c+b^2-2*b-4*c+1)^(1/2))*_C1*a+x^((-4*a*c+b^2-2*b-4*c+1)^(1/2))*_C1-_C2*a-_C2)^2)^(-1/2/(1+a))]