4.18.46 \(x^2 y'(x)^2=y(x)^2\)

ODE
\[ x^2 y'(x)^2=y(x)^2 \] ODE Classification

[_separable]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

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

\[\left \{\left \{y(x)\to \frac {c_1}{x}\right \},\left \{y(x)\to c_1 x\right \}\right \}\]

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

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}}{x}},y \relax (x ) ={\it \_C1}\,x \right \} \] 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