ODE
\[ (1-x) x y''(x)-(x+4) y'(x)+4 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.191503 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {20 c_1 (x-2) x^5+c_2 \left (5 x^2-6 x+2\right )}{20 (x-1)^4}\right \}\right \}\]
Maple ✓
cpu = 0.042 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,x^{5} \left (x -2\right )}{\left (x -1\right )^{4}}+\frac {\textit {\_C2} \left (5 x^{2}-6 x +2\right )}{\left (x -1\right )^{4}}\right ]\] Mathematica raw input
DSolve[4*y[x] - (4 + x)*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (20*(-2 + x)*x^5*C[1] + (2 - 6*x + 5*x^2)*C[2])/(20*(-1 + x)^4)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-(4+x)*diff(y(x),x)+4*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/(x-1)^4*x^5*(x-2)+_C2/(x-1)^4*(5*x^2-6*x+2)]