2.1614   ODE No. 1614

\[ 2 a^2 y(x)+3 a y'(x)+y''(x)-2 y(x)^3=0 \]

✓ Mathematica : cpu = 0.975383 (sec), leaf count = 32

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

\[\left \{\left \{y(x)\to -i a c_1 e^{-a x} \text {sn}\left (\left .e^{-a x} c_1+c_2\right |-1\right )\right \}\right \}\]

✓ Maple : cpu = 0.124 (sec), leaf count = 33

dsolve(diff(diff(y(x),x),x)+3*a*diff(y(x),x)-2*y(x)^3+2*a^2*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{2} \operatorname {JacobiSN}\left (\left (-\frac {\sqrt {-{\mathrm e}^{-2 a x}}}{a}+c_{1} \right ) c_{2} , i\right ) {\mathrm e}^{-a x}\]