2.1130   ODE No. 1130

\[ a y(x)+2 x y''(x)+y'(x)=0 \]

✓ Mathematica : cpu = 0.006809 (sec), leaf count = 46

DSolve[a*y[x] + Derivative[1][y][x] + 2*x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \cos \left (\sqrt {2} \sqrt {a} \sqrt {x}\right )+c_2 \sin \left (\sqrt {2} \sqrt {a} \sqrt {x}\right )\right \}\right \}\]

✓ Maple : cpu = 0.029 (sec), leaf count = 31

dsolve(2*x*diff(diff(y(x),x),x)+diff(y(x),x)+a*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{1} \sin \left (\sqrt {x}\, \sqrt {2}\, \sqrt {a}\right )+c_{2} \cos \left (\sqrt {x}\, \sqrt {2}\, \sqrt {a}\right )\]