ODE No. 1300

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

✓ Mathematica : cpu = 0.0087853 (sec), leaf count = 41

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

\[\left \{\left \{y(x)\to a c_1 x+c_2 \left (a x \left (\frac {1}{2} \log (a x+1)-\frac {1}{2} \log (1-a x)\right )-1\right )\right \}\right \}\]

✓ Maple : cpu = 0.049 (sec), leaf count = 31

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

\[y \left (x \right ) = \frac {c_{2} a \ln \left (a x -1\right ) x}{2}-\frac {c_{2} a \ln \left (a x +1\right ) x}{2}+x c_{1} +c_{2}\]