Civil and Environmental Engineering Answers

A large tank initially contains 220 gal of brine where there is dissolved 35lb of salt. Starting

at time t = 0, a brine containing 3lb of dissolved salt per gallon flows into the tank at the rate of

6gal/min is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the

tank at a slower rate of 3gal/min. How much salt is in the tank at the end of 20 min?

According to the data listed at the Philippine Statistics Authority, the Philippine total

population reached 4 billion persons in year 2020 and was then increasing at the rate of 250

thousand persons each day. Assuming that natural population growth at this rate continues, what

will be the population at year 2060?

PART B. Non-Homogenous Linear Differential Equations

7. (D ^ 2 - 3D + 2) * y = (1 + e ^ (- x)) ^ 2

6. (D ^ 2 + 1) * y = x * cos x

PART B. Non-Homogenous Linear Differential Equations

5.(D^ 2 +25)y=sin x+cos 2x

5. (D ^ 2 + 4) * y = tan 2x

Non-Homogenous Linear Differential Equations

1. (2D ^ 2 + 3D + 1) * y = e ^ (- 3x)

2.(D^ 2 -2D+5)y=25x^ 2 +12

4. (D ^ 2 - 3D + 2) * y = 14sin 2x - 18cos 2x

Homogenous Linear Differential Equations

6. (D ^ 3 - 2D ^ 2 - 3D) * y = 0

5. (D ^ 3 - 3D ^ 2 + 4) * y = 0

7. (4D ^ 3 - 3D + 1) * y = 0

Homogenous Linear Differential Equations

1. (D ^ 2 + 3D) * y = 0

2.(D ^ 2 + D - 7) * y = 0

PART A. Homogenous Linear Differential Equations

1. (D + 3) ^ 2 * y = 0

2. (D ^ 2 - 4D + 7) * y = 0 3. (D ^ 2 + 3D) * y = 0

PART A. Homogenous Linear differential Equations

1. (D + 3) ^ 2 * y = 0

2. (D ^ 2 - 4D + 7) * y = 0

6. (D ^ 3 - 2D ^ 2 - 3D) * y = 0

7. (4D ^ 3 - 3D + 1) * y = 0

5. (D ^ 3 - 3D ^ 2 + 4) * y = 0

4. (D ^ 2 + D - 7) * y = 0

3. (D ^ 2 + 3D) * y = 0

How much energy is released by the sun in a minute? Use Einstein’s equation for special relativity.