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## Analytical ODE solution without ODE45 or for loop

Asked by Kelly

### Kelly (view profile)

on 28 Jan 2013

I need to solve dN/dt = f*(1-N) - g*N and store the analytical solution in an array

```%values
init = 1;
f = 0.5;
g = 0.4;
delta = 0.01;
```
```%Array for time values
t = 0:delta:10 ;
```

Walter Roberson

### Walter Roberson (view profile)

on 28 Jan 2013

Your equation has no t in the right hand side. Should we assume it is

```dN/dt = f*(1-N(t)) - g*N(t)
```

and when you say "init = 1" do you mean that N(0) = 1, or do you mean N'(0) = 1 ?

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## 1 Answer

### Walter Roberson (view profile)

Answer by Walter Roberson

### Walter Roberson (view profile)

on 28 Jan 2013

Assuming you mean dN/dt = f*(1-N(t)) - g*N(t) and N(0) = 1, then:

```N(t) = 5/9+(4/9)*exp(-(9/10)*t)
```

More generally,

```N(t) = f/(f+g) + exp(-(f+g)*t) * (init - f/(f+g))
```

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