2.1017   ODE No. 1017

\[ \left (e^{2 x}-v^2\right ) y(x)+y''(x)=0 \]

✓ Mathematica : cpu = 0.0156501 (sec), leaf count = 46

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

\[\left \{\left \{y(x)\to c_1 \Gamma (1-v) J_{-v}\left (\sqrt {e^{2 x}}\right )+c_2 \Gamma (v+1) J_v\left (\sqrt {e^{2 x}}\right )\right \}\right \}\]

✓ Maple : cpu = 0.063 (sec), leaf count = 17

dsolve(diff(diff(y(x),x),x)+(exp(2*x)-v^2)*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (v , {\mathrm e}^{x}\right )+c_{2} \operatorname {BesselY}\left (v , {\mathrm e}^{x}\right )\]