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 = 0.0247269 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \sqrt {x} \left (c_2 (x+\log (x))+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {\it \_C2}\,\ln \left ( x \right ) +{\it \_C2}\,x+{\it \_C1} \right ) \right \} \] 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*(1+x)*diff(diff(y(x),x),x)-4*x^2*diff(y(x),x)+(1+3*x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^(1/2)*(_C2*ln(x)+_C2*x+_C1)