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 = 0.00351953 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_1 x^3\right \},\left \{y(x)\to c_1+2 x\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{3},y \left ( x \right ) =2\,x+{\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*x^3, y(x) = 2*x+_C1