- #1
scarebyte
- 11
- 0
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!
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!