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 = 0.00628933 (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 = 0.381 (sec), leaf count = 79
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{1+a}{x}^{{\frac {b}{2}}-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{b}^{2}-2\,b+1+ \left ( -4\,a-4 \right ) c}}}\sqrt {{b}^{2}-2\,b+1+ \left ( -4\,a-4 \right ) c}+{\it \_C1}\, \left ( 1+a \right ) {x}^{\sqrt {{b}^{2}-2\,b+1+ \left ( -4\,a-4 \right ) c}}+{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
y(x)^(1+a)*x^(1/2*b-1/2+1/2*(b^2-2*b+1+(-4*a-4)*c)^(1/2))*(b^2-2*b+1+(-4*a-4)*c)^(1/2)+_C1*(1+a)*x^((b^2-2*b+1+(-4*a-4)*c)^(1/2))+_C2 = 0