ODE No. 1098

\[ -a x^3 y(x)+x y''(x)-y'(x)=0 \]

✓ Mathematica : cpu = 0.0062101 (sec), leaf count = 41

DSolve[-(a*x^3*y[x]) - Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to c_1 \cosh \left (\frac {\sqrt {a} x^2}{2}\right )+i c_2 \sinh \left (\frac {\sqrt {a} x^2}{2}\right )\right \}\right \}\]

✓ Maple : cpu = 0.019 (sec), leaf count = 27

dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)-y(x)*a*x^3=0,y(x))

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