4.7.13 \((1-x) x y'(x)=a+(x+1) y(x)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0123901 (sec), leaf count = 24

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

Maple
cpu = 0.021 (sec), leaf count = 23

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = (-a*ln(x)*x+_C1*x-a)/(-1+x)^2