ODE
\[ x y'(x)^2-(3 y(x)+2 x) y'(x)+6 y(x)=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.160972 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_1 x^3\right \},\{y(x)\to 2 x+c_1\}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 17
\[[y \left (x \right ) = 2 x +\textit {\_C1}, y \left (x \right ) = \textit {\_C1} \,x^{3}]\] Mathematica raw input
DSolve[6*y[x] - (2*x + 3*y[x])*y'[x] + x*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^3*C[1]}, {y[x] -> 2*x + C[1]}}
Maple raw input
dsolve(x*diff(y(x),x)^2-(2*x+3*y(x))*diff(y(x),x)+6*y(x) = 0, y(x))
Maple raw output
[y(x) = 2*x+_C1, y(x) = _C1*x^3]