4.7.19 \((1-x) x y'(x)-3 x y(x)+y(x)+2=0\)

ODE
\[ (1-x) x y'(x)-3 x y(x)+y(x)+2=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00756792 (sec), leaf count = 23

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

Maple
cpu = 0.016 (sec), leaf count = 21

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

DSolve[2 + y[x] - 3*x*y[x] + (1 - x)*x*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*(1-x)*diff(y(x),x)+2-3*x*y(x)+y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (x^2+_C1-2*x)/(-1+x)^2/x