4.7.18 \((1-x) x y'(x)=a+2 (2-x) y(x)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0109021 (sec), leaf count = 29

\[\left \{\left \{y(x)\to \frac {a (4 x-3)+12 c_1 x^4}{12 (x-1)^2}\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 25

\[ \left \{ y \relax (x ) ={\frac {12\,{\it \_C1}\,{x}^{4}+4\,ax-3\,a}{12\, \left (-1+x \right ) ^{2}}} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (a*(-3 + 4*x) + 12*x^4*C[1])/(12*(-1 + x)^2)}}

Maple raw input

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

Maple raw output

y(x) = 1/12*(12*_C1*x^4+4*a*x-3*a)/(-1+x)^2