4.7.14 \((1-x) x y'(x)=2 (x y(x)+1)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00624863 (sec), leaf count = 21

\[\left \{\left \{y(x)\to \frac {c_1-2 x+2 \log (x)}{(x-1)^2}\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 19

\[ \left \{ y \relax (x ) ={\frac {-2\,x+2\,\ln \relax (x ) +{\it \_C1}}{ \left (-1+x \right ) ^{2}}} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (-2*x + C[1] + 2*Log[x])/(-1 + x)^2}}

Maple raw input

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

Maple raw output

y(x) = (-2*x+2*ln(x)+_C1)/(-1+x)^2