4.19.13 $x^2{y}^{\prime }(x{)}^2-5xy(x)y^{\prime }(x)+6y(x{)}^2=0$

ODE
$$x^2{y}^{\prime }(x{)}^2-5xy(x)y^{\prime }(x)+6y(x{)}^2=0$$ ODE Classification

[_separable]

Book solution method
No Missing Variables ODE, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.00432365 (sec), leaf count = 21

$$\{\{y(x)\to c_1{x}^2\},\{y(x)\to c_1{x}^3\}\}$$

Maple ✓
cpu = 0.012 (sec), leaf count = 17

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^2,y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^3\}$$ 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