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 = 0.233478 (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 = 0.223 (sec), leaf count = 54
\[\left [y \left (x \right ) = \frac {\sqrt {-x \left (-a \,x^{2}+2 \textit {\_C1} x -2 \textit {\_C2} \right )}}{x^{2}}, y \left (x \right ) = -\frac {\sqrt {-x \left (-a \,x^{2}+2 \textit {\_C1} x -2 \textit {\_C2} \right )}}{x^{2}}\right ]\] 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))
Maple raw output
[y(x) = 1/x^2*(-x*(-a*x^2+2*_C1*x-2*_C2))^(1/2), y(x) = -1/x^2*(-x*(-a*x^2+2*_C1*x-2*_C2))^(1/2)]