\[ a y(x)^3 \phi '(x)+\frac {(2 a+1) y(x) \phi ''(x)}{\phi '(x)}+6 a \phi (x) y(x)^2+2 a+y'(x)+2=0 \] ✗ Mathematica : cpu = 25.454 (sec), leaf count = 0
DSolve[2 + 2*a + 6*a*phi[x]*y[x]^2 + a*y[x]^3*Derivative[1][phi][x] + Derivative[1][y][x] + ((1 + 2*a)*y[x]*Derivative[2][phi][x])/Derivative[1][phi][x] == 0,y[x],x]
, could not solve
DSolve[2 + 2*a + 6*a*phi[x]*y[x]^2 + a*y[x]^3*Derivative[1][phi][x] + Derivative[1][y][x] + ((1 + 2*a)*y[x]*Derivative[2][phi][x])/Derivative[1][phi][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(y(x),x)+a*diff(phi(x),x)*y(x)^3+6*a*phi(x)*y(x)^2+(2*a+1)*y(x)*diff(diff(phi(x),x),x)/diff(phi(x),x)+2*a+2 = 0,y(x))
, could not solve
dsolve(diff(y(x),x)+a*diff(phi(x),x)*y(x)^3+6*a*phi(x)*y(x)^2+(2*a+1)*y(x)*diff(diff(phi(x),x),x)/diff(phi(x),x)+2*a+2 = 0,y(x))