4.18.46 $x^2{y}^{\prime }(x{)}^2=y(x{)}^2$

ODE
$$x^2{y}^{\prime }(x{)}^2=y(x{)}^2$$ ODE Classification

[_separable]

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

Mathematica ✓
cpu = 0.00403022 (sec), leaf count = 19

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

Maple ✓
cpu = 0.009 (sec), leaf count = 15

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

DSolve[x^2*y'[x]^2 == y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/x}, {y[x] -> x*C[1]}}

Maple raw input

dsolve(x^2*diff(y(x),x)^2 = y(x)^2, y(x),'implicit')

Maple raw output

y(x) = _C1/x, y(x) = _C1*x