ODE
\[ x y(x) y''(x)+x y'(x)^2=3 y(x) y'(x) \] ODE Classification
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.310964 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 \sqrt {x^4+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.101 (sec), leaf count = 35
\[\left [y \left (x \right ) = -\frac {\sqrt {2 \textit {\_C1} \,x^{4}+8 \textit {\_C2}}}{2}, y \left (x \right ) = \frac {\sqrt {2 \textit {\_C1} \,x^{4}+8 \textit {\_C2}}}{2}\right ]\] Mathematica raw input
DSolve[x*y'[x]^2 + x*y[x]*y''[x] == 3*y[x]*y'[x],y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x^4 + 2*C[1]]*C[2]}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x)+x*diff(y(x),x)^2 = 3*y(x)*diff(y(x),x), y(x))
Maple raw output
[y(x) = -1/2*(2*_C1*x^4+8*_C2)^(1/2), y(x) = 1/2*(2*_C1*x^4+8*_C2)^(1/2)]