2.1143   ODE No. 1143

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

✓ Mathematica : cpu = 0.019192 (sec), leaf count = 93

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

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

✓ Maple : cpu = 0.181 (sec), leaf count = 57

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

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