How to solve this differntial equation? dy/dt = (2-y)(5-y)

[sonithcob]

How to solve this differntial equation?

dy/dt = (2-y)(5-y)

 

[Deleted member 4993]

How to solve this differntial equation?

dy/dt = (2-y)(5-y)

Hint:

\(\displaystyle \dfrac{1}{(2-y)(5-y)} \ = \ \dfrac{1}{3} * \left [ \dfrac{1}{2-y} \ - \ \dfrac{1}{5-y} \right ] \)

 

[stapel]

How to solve this differntial equation?

dy/dt = (2-y)(5-y)

In case you're not sure what's going on in the first reply you received, think "partial fractions" (here).

 

[oscarguevara]

How to solve this differntial equation?

dy/dt = (2-y)(5-y)

dt= - (2-y) + (5-y) -2 /(2-y)(5-y)
t=ln(5-y)/(2-y)
2e^t - ye^t=5-y
2e^t -5= y(e^t - 1)
y=(2e^t -5)/y(e^t - 1) i allways forget the constant