2.1187   ODE No. 1187

\[ a x y'(x)+b y(x)+x^2 y''(x)=0 \] Mathematica : cpu = 0.0072039 (sec), leaf count = 99

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

\[\left \{\left \{y(x)\to c_1 x^{\frac {1}{2} \sqrt {b} \left (-\frac {\sqrt {a^2-2 a-4 b+1}}{\sqrt {b}}-\frac {a-1}{\sqrt {b}}\right )}+c_2 x^{\frac {1}{2} \sqrt {b} \left (\frac {\sqrt {a^2-2 a-4 b+1}}{\sqrt {b}}-\frac {a-1}{\sqrt {b}}\right )}\right \}\right \}\] Maple : cpu = 0.016 (sec), leaf count = 53

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

\[y \left (x \right ) = c_{1} x^{-\frac {a}{2}+\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}}+c_{2} x^{-\frac {a}{2}+\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}}\]