ODE
\[ 4 (x+1) x^2 y''(x)-4 x^2 y'(x)+(3 x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.172311 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \sqrt {x} (c_2 (x+\log (x))+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.055 (sec), leaf count = 19
\[\left [y \left (x \right ) = \textit {\_C1} \sqrt {x}+\textit {\_C2} \sqrt {x}\, \left (x +\ln \left (x \right )\right )\right ]\] Mathematica raw input
DSolve[(1 + 3*x)*y[x] - 4*x^2*y'[x] + 4*x^2*(1 + x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*(C[1] + C[2]*(x + Log[x]))}}
Maple raw input
dsolve(4*x^2*(x+1)*diff(diff(y(x),x),x)-4*x^2*diff(y(x),x)+(1+3*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(1/2)+_C2*x^(1/2)*(x+ln(x))]