2.1018   ODE No. 1018

\[ a e^{b x} y(x)+y''(x)=0 \]

✓ Mathematica : cpu = 0.0135391 (sec), leaf count = 55

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

\[\left \{\left \{y(x)\to c_1 J_0\left (\frac {2 \sqrt {a} \sqrt {e^{b x}}}{b}\right )+2 c_2 Y_0\left (\frac {2 \sqrt {a} \sqrt {e^{b x}}}{b}\right )\right \}\right \}\]

✓ Maple : cpu = 0.106 (sec), leaf count = 39

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

\[y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (0, \frac {2 \sqrt {a}\, {\mathrm e}^{\frac {b x}{2}}}{b}\right )+c_{2} \operatorname {BesselY}\left (0, \frac {2 \sqrt {a}\, {\mathrm e}^{\frac {b x}{2}}}{b}\right )\]