2.1132   ODE No. 1132

\[ a y(x)+2 x y''(x)-(2 x-1) y'(x)=0 \]

✓ Mathematica : cpu = 0.0071261 (sec), leaf count = 48

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

\[\left \{\left \{y(x)\to c_1 \sqrt {x} U\left (\frac {1-a}{2},\frac {3}{2},x\right )+c_2 \sqrt {x} L_{\frac {a-1}{2}}^{\frac {1}{2}}(x)\right \}\right \}\]

✓ Maple : cpu = 0.131 (sec), leaf count = 29

dsolve(2*x*diff(diff(y(x),x),x)-(2*x-1)*diff(y(x),x)+a*y(x)=0,y(x))
 

\[y \left (x \right ) = \sqrt {x}\, \left (\operatorname {KummerU}\left (-\frac {a}{2}+\frac {1}{2}, \frac {3}{2}, x\right ) c_{2} +\operatorname {KummerM}\left (-\frac {a}{2}+\frac {1}{2}, \frac {3}{2}, x\right ) c_{1} \right )\]