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 = 0.17726 (sec), leaf count = 21

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

Maple
cpu = 0.006 (sec), leaf count = 19

\[\left [y \left (x \right ) = \frac {-2 x +2 \ln \left (x \right )+\textit {\_C1}}{\left (x -1\right )^{2}}\right ]\] 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))

Maple raw output

[y(x) = (-2*x+2*ln(x)+_C1)/(x-1)^2]