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 = 0.184542 (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 = 0.057 (sec), leaf count = 36
\[\left [y \left (x \right ) = \left (-\frac {2 \textit {\_C1} \left (8 x^{2}+12 x +3\right )}{3 \sqrt {x}\, \left (x +1\right )^{\frac {3}{2}}}+\textit {\_C2} \right ) \sqrt {x}\, \left (x +1\right )^{\frac {3}{2}}\right ]\] 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*(x+1)*diff(diff(y(x),x),x)+diff(y(x),x)-4*y(x) = 0, y(x))
Maple raw output
[y(x) = (-2/3*_C1*(8*x^2+12*x+3)/x^(1/2)/(x+1)^(3/2)+_C2)*x^(1/2)*(x+1)^(3/2)]