ODE
\[ (1-x) x y''(x)-(x+4) y'(x)+4 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0402533 (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 = 0.021 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{6}-2\,{\it \_C1}\,{x}^{5}+5\,{\it \_C2}\,{x}^{2}-6\,{\it \_C2}\,x+2\,{\it \_C2}}{ \left ( -1+x \right ) ^{4}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (_C1*x^6-2*_C1*x^5+5*_C2*x^2-6*_C2*x+2*_C2)/(-1+x)^4