4.19.11 $x^2{y}^{\prime }(x{)}^2+4xy(x)y^{\prime }(x)-5y(x{)}^2=0$

ODE
$$x^2{y}^{\prime }(x{)}^2+4xy(x)y^{\prime }(x)-5y(x{)}^2=0$$ ODE Classification

[_separable]

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

Mathematica ✓
cpu = 0.00461228 (sec), leaf count = 19

$$\{\{y(x)\to \frac{c_1}{x^5}\},\{y(x)\to c_{1}x\}\}$$

Maple ✓
cpu = 0.01 (sec), leaf count = 15

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x^5},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x\}$$ Mathematica raw input

DSolve[-5*y[x]^2 + 4*x*y[x]*y'[x] + x^2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/x^5}, {y[x] -> x*C[1]}}

Maple raw input

dsolve(x^2*diff(y(x),x)^2+4*x*y(x)*diff(y(x),x)-5*y(x)^2 = 0, y(x),'implicit')

Maple raw output

y(x) = _C1/x^5, y(x) = _C1*x