Problem 1.

The population of rabbits in a farm satisfies the logistic growth model $\frac{\mathrm{d} N}{\mathrm{~d} t}=5 N\left(8-\frac{N}{10}\right)$, where $t$ is measured in hours and the initial population is 30 .
i) What is the carrying capacity of the population? Answer:

ii) What will the population’s size be when the population is growing the fastest?
$N=50$
$N=40$
$N=30$
$N=60$

Problem 2.

Find the value of $a$ such that the function
$$y=a x^2-7$$
satisfies the differential equation
$$x y^{\prime}-y+3(x-3)^2=34-18 x$$
$$a=\text { 数字 }$$

Problem 3.

The ordinary differential equation
$$y^{\prime \prime}=y^{\prime} t^2+3 y-2$$
is linear.
TRUE
FALSE

Problem 4.

Find the general solutions of:
$$\frac{d y}{d x}+2 x y=6 x$$
Write your answer in the form $y=$ expression. Use ” $C^{\prime \prime}$ as your constant of integration. If necessary use $\exp \left(z^{\wedge} 2\right)$ for $e^{z^2}$.

real analysis代写analysis 2, analysis 3请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。

Picard定理，ODE存在唯一性介绍