ODE
\[ x^3 y(x) y''(x)+x^3 y'(x)^2+6 x^2 y(x) y'(x)+3 x y(x)^2=a \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0891561 (sec), leaf count = 58
\[\left \{\left \{y(x)\to -\frac {\sqrt {a x^2+c_2 x+2 c_1}}{x^{3/2}}\right \},\left \{y(x)\to \frac {\sqrt {a x^2+c_2 x+2 c_1}}{x^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.035 (sec), leaf count = 24
\[ \left \{ -{\frac {ax}{2}}+{\frac {{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}{2}}+{\it \_C2}-{\frac {{\it \_C1}}{x}}=0 \right \} \] Mathematica raw input
DSolve[3*x*y[x]^2 + 6*x^2*y[x]*y'[x] + x^3*y'[x]^2 + x^3*y[x]*y''[x] == a,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[a*x^2 + 2*C[1] + x*C[2]]/x^(3/2))}, {y[x] -> Sqrt[a*x^2 + 2*C[1] + x*C[2]]/x^(3/2)}}
Maple raw input
dsolve(x^3*y(x)*diff(diff(y(x),x),x)+x^3*diff(y(x),x)^2+6*x^2*y(x)*diff(y(x),x)+3*x*y(x)^2 = a, y(x),'implicit')
Maple raw output
-1/2*a*x+1/2*x^2*y(x)^2+_C2-1/x*_C1 = 0