ODE
\[ (1-x) x y''(x)-2 (2 x+1) y'(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0317103 (sec), leaf count = 52
\[\left \{\left \{y(x)\to \frac {-3 c_2 x^4-3 c_1 x^3+12 c_2 x^3 \log (x)+18 c_2 x^2-6 c_2 x+c_2}{3 (x-1)^5}\right \}\right \}\]
Maple ✓
cpu = 0.031 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac {12\,\ln \left ( x \right ) {\it \_C1}\,{x}^{3}+ \left ( -3\,{x}^{4}+18\,{x}^{2}-6\,x+1 \right ) {\it \_C1}+{x}^{3}{\it \_C2}}{ \left ( -1+x \right ) ^{5}}} \right \} \] Mathematica raw input
DSolve[-2*y[x] - 2*(1 + 2*x)*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-3*x^3*C[1] + C[2] - 6*x*C[2] + 18*x^2*C[2] - 3*x^4*C[2] + 12*x^3*C[2]*Log[x])/(3*(-1 + x)^5)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-2*(1+2*x)*diff(y(x),x)-2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (12*ln(x)*_C1*x^3+(-3*x^4+18*x^2-6*x+1)*_C1+x^3*_C2)/(-1+x)^5