Differential equation

[Rodrik]

Some help for first step?

 

[Deleted member 4993]

View attachment 23129
Some help for first step?

What is the Homogeneous solution of your DE? That would be my first step.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Deleted member 4993]

View attachment 23129
Some help for first step?

Can you solve:

$\displaystyle \frac{dN}{N - N^2 } \ = \ dt$ ...............[edited]

 

[HallsofIvy]

There is a standard "reduction of order" method. I suspect that this problem was designed to test that! Since you are told that $\displaystyle \frac{1}{t}+\frac{1}{2}$ is a solution to this differential equation, try a solution of the form $\displaystyle u(t)\left(\frac{1}{t}+ \frac{1}{2}\right)= \frac{u(t)}{t}+ \frac{u(t)}{2}$ and try to determine u.