4.7.16 \(x (x+1) y'(x)=(1-2 x) y(x)\)

ODE
\[ x (x+1) y'(x)=(1-2 x) y(x) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00784502 (sec), leaf count = 14

\[\left \{\left \{y(x)\to \frac {c_1 x}{(x+1)^3}\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 12

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}\,x}{ \left (1+x \right ) ^{3}}} \right \} \] Mathematica raw input

DSolve[x*(1 + x)*y'[x] == (1 - 2*x)*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (x*C[1])/(1 + x)^3}}

Maple raw input

dsolve(x*(1+x)*diff(y(x),x) = (1-2*x)*y(x), y(x),'implicit')

Maple raw output

y(x) = _C1/(1+x)^3*x