Given a general solution, find the EDO

[scarebyte]

1. The problem statement

Given the general solution:
y==(2*c*e^(2x)) / (1+c*e^(2x))
find the EDO.

2. The attempt at a solution

Im tried isolate c*e^(2x), using implicit differentiation:

y + y*c*e^(2x)==2*c*e^(2x)
y'+y'*c*e^2x + 2*y*c*e^(2x)==2*2*c*e^(2x)
y'==c*e^(2x) * (4-y'-2y)
e^(2x) * c = y'/(4-y'-2*y)

Replacing in the general solution given in the problem statement i have this EDO:

y==[y'/(4-y'-2*y)]*(2-y)

But, in mathematica software when i use DSolve over this EDO to find the general solution, it gives a different one.

What's wrong?

Thanks!

 

[HallsofIvy]

1. The problem statement

Given the general solution:
y==(2*c*e^(2x)) / (1+c*e^(2x))
find the EDO.

2. The attempt at a solution

Im tried isolate c*e^(2x), using implicit differentiation:

y + y*c*e^(2x)==2*c*e^(2x)
y'+y'*c*e^2x + 2*y*c*e^(2x)==2*2*c*e^(2x)
y'==c*e^(2x) * (4-y'-2y)
e^(2x) * c = y'/(4-y'-2*y)

Replacing in the general solution given in the problem statement i have this EDO:

y==[y'/(4-y'-2*y)]*(2-y)

But, in mathematica software when i use DSolve over this EDO to find the general solution, it gives a different one.

What's wrong?

Thanks!

There is nothing wrong. I suspect that DSolve is just giving a different, equivalent way of writing the solution.