Differential Equations: Problem Set 3

(2.1) 11, 14, 18, 20, 22

Solve the IVP:

$$x^{\prime }=x(4+x),x\left(0\right)=1$$

Hint: use a partial fraction decomposition

Solve the logistic growth equation:

$$N^{\prime }=rN\left(1-\frac{N}{K}\right),N\left(0\right)=N_0$$