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