4.19.11 \(x^2 y'(x)^2+4 x y(x) y'(x)-5 y(x)^2=0\)

ODE
\[ x^2 y'(x)^2+4 x y(x) y'(x)-5 y(x)^2=0 \] ODE Classification

[_separable]

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

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

\[\left \{\left \{y(x)\to \frac {c_1}{x^5}\right \},\left \{y(x)\to c_1 x\right \}\right \}\]

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

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}}{{x}^{5}}},y \relax (x ) ={\it \_C1}\,x \right \} \] 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