ODE
\[ 2 x (x+1) y''(x)+y'(x)-4 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.911551 (sec), leaf count = 37
\[\left \{\left \{y(x)\to c_1 \sqrt {x} (x+1)^{3/2}-\frac {2}{3} c_2 \left (8 x^2+12 x+3\right )\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={\it \_C2}\, \left ( 1+x \right ) ^{{\frac {3}{2}}}\sqrt {x}-{\frac {16\,{\it \_C1}}{3} \left ( {x}^{2}+{\frac {3\,x}{2}}+{\frac {3}{8}} \right ) } \right \} \] Mathematica raw input
DSolve[-4*y[x] + y'[x] + 2*x*(1 + x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*(1 + x)^(3/2)*C[1] - (2*(3 + 12*x + 8*x^2)*C[2])/3}}
Maple raw input
dsolve(2*x*(1+x)*diff(diff(y(x),x),x)+diff(y(x),x)-4*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C2*(1+x)^(3/2)*x^(1/2)-16/3*(x^2+3/2*x+3/8)*_C1