ODE
\[ 2 x^2 y''(x)-(2 x+7) x y'(x)+2 (x+5) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.186718 (sec), leaf count = 40
\[\left \{\left \{y(x)\to c_1 e^x x^{5/2}+2 c_2 x^2 \left (e^x \sqrt {x} \Gamma \left (\frac {1}{2},x\right )-1\right )\right \}\right \}\]
Maple ✓
cpu = 0.622 (sec), leaf count = 33
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{\frac {5}{2}} {\mathrm e}^{x}+\textit {\_C2} \left (\sqrt {\pi }\, {\mathrm e}^{x} \left (\erf \left (\sqrt {x}\right )-1\right ) x^{\frac {5}{2}}+x^{2}\right )\right ]\] Mathematica raw input
DSolve[2*(5 + x)*y[x] - x*(7 + 2*x)*y'[x] + 2*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*x^(5/2)*C[1] + 2*x^2*C[2]*(-1 + E^x*Sqrt[x]*Gamma[1/2, x])}}
Maple raw input
dsolve(2*x^2*diff(diff(y(x),x),x)-x*(7+2*x)*diff(y(x),x)+2*(5+x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(5/2)*exp(x)+_C2*(Pi^(1/2)*exp(x)*(erf(x^(1/2))-1)*x^(5/2)+x^2)]