ODE
\[ x^2 y'(x)^2-5 x y(x) y'(x)+6 y(x)^2=0 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.187163 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_1 x^2\right \},\left \{y(x)\to c_1 x^3\right \}\right \}\]
Maple ✓
cpu = 0.057 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} \,x^{3}, y \left (x \right ) = x^{2} \textit {\_C1}]\] Mathematica raw input
DSolve[6*y[x]^2 - 5*x*y[x]*y'[x] + x^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2*C[1]}, {y[x] -> x^3*C[1]}}
Maple raw input
dsolve(x^2*diff(y(x),x)^2-5*x*y(x)*diff(y(x),x)+6*y(x)^2 = 0, y(x))
Maple raw output
[y(x) = _C1*x^3, y(x) = x^2*_C1]