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 = 0.181466 (sec), leaf count = 19
\[\left \{\left \{y(x)\to \frac {c_1}{x^5}\right \},\{y(x)\to c_1 x\}\right \}\]
Maple ✓
cpu = 0.053 (sec), leaf count = 15
\[\left [y \left (x \right ) = x \textit {\_C1}, y \left (x \right ) = \frac {\textit {\_C1}}{x^{5}}\right ]\] 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))
Maple raw output
[y(x) = x*_C1, y(x) = _C1/x^5]