Exam 9: Differential Equations

A population is modeled by the differential equation. For what values of P is the population increasing?

Select the correct Answer: for each question. - be a positive number.A differential equation of the form where is a positive constant is called a doomsday equation because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term .If such rabbits breed initially and the warren has rabbits after months, then when is doomsday?

Determine whether the differential equation is linear.

Let What are the equilibrium solutions?

Find the orthogonal trajectories of the family of curves.

Solve the differential equation.

Solve the differential equation.

In the circuit shown in Figure, a generator supplies a voltage of volts, the inductance is 2 H, the resistance is 40 , and Find the current 0.2 s after the switch is closed.Round yourAnswer to two decimal places.

We modeled populations of aphids and ladybugs with a Lotka-Volterra system.Suppose we modify those equations as follows: Find the equilibrium solution.

A sum of is invested at interest.If is the amount of the investment at time for the case of continuous compounding, write a differential equation and an initial condition satisfied by

A population is modeled by the differential equation For what values of is the population decreasing?

Solve the initial-value problem.

Solve the differential equation.

Solve the differential equation.

Kirchhoff's Law gives us the derivative equation If use Euler's method with step size 0.1 to estimate after 0.3 second.

We modeled populations of aphids and ladybugs with a Lotka-Volterra system.Suppose we modify those equations as follows: Find the equilibrium solution.

Select the correct Answer: for each question. -A population is modeled by the differential equation. For what values of P is the population increasing?

Solve the initial-value problem.

Determine whether the differential equation is linear.Select the correct Answer

Which equation does the function satisfy? Select the correct Answer