ODE
\[ 4 x^2 y''(x)-2 (x+2) x y'(x)+(x+3) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.168769 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \sqrt {x} \left (2 c_2 e^{x/2}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.068 (sec), leaf count = 19
\[\left [y \left (x \right ) = \textit {\_C1} \sqrt {x}+\textit {\_C2} \sqrt {x}\, {\mathrm e}^{\frac {x}{2}}\right ]\] Mathematica raw input
DSolve[(3 + x)*y[x] - 2*x*(2 + x)*y'[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*(C[1] + 2*E^(x/2)*C[2])}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)-2*x*(2+x)*diff(y(x),x)+(3+x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(1/2)+_C2*x^(1/2)*exp(1/2*x)]