2

1. Solve the following differential equation:

y′′(x) + 6y′(x) + 25y(x) = 0.

3

2. Consider a linear differential equation

ay′′ + by′ + cy = f(x)

with constant coefficients. Let y1(x), y2(x) be solutions to the homogeneous equation

ay′′ + by′ + cy = 0

and let yp(x) be a particular solution

Prove that C1y1 + C2y2 + yp is a solution for any choice of constants C1, C2.

4

3. A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t = 0, city wate

containing 0.001% chlorine is pumped into the pool at a rate of 5 gal/min. The pool water flows out at the same rate.

What is the percentage of chlorine in the pool after 1 h? When will the pool water be 0.002% chlorine?

5

4. There are infinitely many different solutions to y′′ − y = 0 with conditions

y(0) = 0 and y′(0) = 1.

This is TRUE / FALSE.

Reason:

5. Solve the following differential equation:

6

y′′′ + y′′ + 4y′ + 4y = 0.

7

6. Find the general solution of the differential equation:

y′′′ − y′′ + y′ − 1 = 0

8

7.

(a) Draw a phase line diagram for the differential equation

dx/dt = (2 − 5x)3(1 − 2x)(1 − 4x2).

Expected in the diagram are equili

ium points and signs of x′ (or flow direction

markers < and >).

(b) Draw a phase diagram using the phase line diagram of (a). Add these labels as

appropriate: funnel, spout, node, stable, unstable. Show at least 10 threaded curves. A

direction field is not required.

Answered Same DayFeb 19, 2022

a) The percentage of chlorine after 1 hour is 0.00973%.

) The pool water will habe a concentration of 0.002% chlorine at 4394 minutes (or 73.24 hours).

Step-by-step explanation:

We can define as X(t) the amount of chlorine that is in the pool at time t.

Then, the rate of change of X can be...

) The pool water will habe a concentration of 0.002% chlorine at 4394 minutes (or 73.24 hours).

Step-by-step explanation:

We can define as X(t) the amount of chlorine that is in the pool at time t.

Then, the rate of change of X can be...

SOLUTION.PDF## Answer To This Question Is Available To Download

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