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 = 0.173369 (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 = 0.047 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}, y \left (x \right ) = \frac {\textit {\_C1}}{x^{2}}\right ]\] 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))
Maple raw output
[y(x) = 1/x*_C1, y(x) = _C1/x^2]