2.1170   ODE No. 1170

\[ y(x) \left (a x^2+b\right )+x^2 y''(x)+2 x y'(x)=0 \]

✓ Mathematica : cpu = 0.0123349 (sec), leaf count = 58

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

\[\left \{\left \{y(x)\to c_1 j_{\frac {1}{2} \left (\sqrt {1-4 b}-1\right )}\left (\sqrt {a} x\right )+c_2 y_{\frac {1}{2} \left (\sqrt {1-4 b}-1\right )}\left (\sqrt {a} x\right )\right \}\right \}\]

✓ Maple : cpu = 0.059 (sec), leaf count = 43

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

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