2.1297   ODE No. 1297

\[ \left (a x^2+1\right ) y''(x)+a x y'(x)+b y(x)=0 \]

✓ Mathematica : cpu = 0.048203 (sec), leaf count = 74

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

\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {\sqrt {b} \tanh ^{-1}\left (\frac {\sqrt {a} x}{\sqrt {a x^2+1}}\right )}{\sqrt {a}}\right )+c_2 \sin \left (\frac {\sqrt {b} \tanh ^{-1}\left (\frac {\sqrt {a} x}{\sqrt {a x^2+1}}\right )}{\sqrt {a}}\right )\right \}\right \}\]

✓ Maple : cpu = 0.061 (sec), leaf count = 63

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

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