4.19.13 \(x^2 y'(x)^2-5 x y(x) y'(x)+6 y(x)^2=0\)

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 = 0.00432365 (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 = 0.012 (sec), leaf count = 17

\[ \left \{ y \relax (x ) ={\it \_C1}\,{x}^{2},y \relax (x ) ={\it \_C1}\,{x}^{3} \right \} \] 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),'implicit')

Maple raw output

y(x) = _C1*x^2, y(x) = _C1*x^3