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 = 0.0406546 (sec), leaf count = 46
\[\left \{\left \{y(x)\to c_1 e^x x^{5/2}-2 c_2 x^2 \left (\sqrt {\pi } e^x \sqrt {x} \text {erf}\left (\sqrt {x}\right )+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.108 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}} \left ( {\it \_C2}\,\sqrt {\pi }{\it Erf} \left ( \sqrt {x} \right ) -{\it \_C2}\,\sqrt {\pi }+{\it \_C1} \right ) {x}^{{\frac {5}{2}}}+{\it \_C2}\,{x}^{2} \right \} \] 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[Pi]*Sqrt[x]*Erf[Sqrt[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),'implicit')
Maple raw output
y(x) = exp(x)*(_C2*Pi^(1/2)*erf(x^(1/2))-_C2*Pi^(1/2)+_C1)*x^(5/2)+_C2*x^2