4.19.9 \(x^2 y'(x)^2+3 x y(x) y'(x)+2 y(x)^2=0\)

ODE
\[ x^2 y'(x)^2+3 x y(x) y'(x)+2 y(x)^2=0 \] ODE Classification

[_separable]

Book solution method
Homogeneous ODE, \(x^n f\left (\frac {y}{x} , y' \right )=0\), Solve for \(p\)

Mathematica
cpu = 0.00487243 (sec), leaf count = 21

\[\left \{\left \{y(x)\to \frac {c_1}{x^2}\right \},\left \{y(x)\to \frac {c_1}{x}\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 17

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}}{{x}^{2}}},y \relax (x ) ={\frac {{\it \_C1}}{x}} \right \} \] Mathematica raw input

DSolve[2*y[x]^2 + 3*x*y[x]*y'[x] + x^2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/x^2}, {y[x] -> C[1]/x}}

Maple raw input

dsolve(x^2*diff(y(x),x)^2+3*x*y(x)*diff(y(x),x)+2*y(x)^2 = 0, y(x),'implicit')

Maple raw output

y(x) = _C1/x, y(x) = _C1/x^2