ODE No. 1752

\[ a y(x)^2+4 y(x) y''(x)-5 y'(x)^2=0 \]

✓ Mathematica : cpu = 0.187002 (sec), leaf count = 26

DSolve[a*y[x]^2 - 5*Derivative[1][y][x]^2 + 4*y[x]*Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to c_2 \text {sech}^4\left (\frac {1}{4} \sqrt {a} (x-4 c_1)\right )\right \}\right \}\]

✓ Maple : cpu = 0.269 (sec), leaf count = 33

dsolve(4*diff(diff(y(x),x),x)*y(x)-5*diff(y(x),x)^2+a*y(x)^2=0,y(x))

\[y \left (x \right ) = \frac {16 \,{\mathrm e}^{\sqrt {a}\, x} a^{2}}{\left (c_{1} {\mathrm e}^{\frac {\sqrt {a}\, x}{2}}-c_{2} \right )^{4}}\]