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4 years ago

SOLVE. y''+3y'+2y=4e^x

1 answer:

8 0

This a second order linear differential equation with the solution given by the general solution + the particular solution.
The general solution is given by Ae^mx + Be^nx; where m and n are solutions to the quadratic equation t^2 + 3t + 2 = 0
(t + 1)(t + 2) = 0
t = -1 or t = -2
general solution = Ae^(-x) + Be^(-2x)
For the particular solution, Ce^x + 3Ce^x + 2Ce^x = 4e^x
6Ce^x = 4e^x
C = 4/6 = 2/3

Therefore, solution is y = Ae^(-x) + Be^(-2x) + 2/3e^x

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4 years ago

Please complete that attachment attached below

Varvara68 [4.7K]

Answer:

Question 9

Step-by-step explanation:

9a:

i. 23

ii. 195

iii. 2.76

9b:

i. 32, 83, 4.35

ii. 14, 11, 2.46

4 0

3 years ago

Read 2 more answers

Suzette deposited $800 into a bank account earning simple interest of 2.5% each year. After 5 years, how much interest had her a

Blababa [14]

Answer:

$\boxed {\boxed {\sf \$ 100.00}}$

Step-by-step explanation:

The formula for simple interest is

$I=prt$

where p is the principal, r is the rate, and t is the time.

The principal, or initial amount is $800 and the time is 5 years The interest rate is 2.5%, but we must convert to a decimal.

Divide by 100 or move the decimal place two spots to the left.

2.5/100=0.025 or 2.5 ⇒ 0.25 ⇒ 0.025

Substitute the known values into the formula.

$p= 800 \\r= 0.025 \\t= 5$

$I= (800)(0.025)(5)$

Multiply.

$I=20(5)\\I=100$

After 5 years, Suzette's account has earned $100.00

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3 years ago

Katenka cross country skied a trail that was 3/4 mile each way. after skiing 2/3 of the trail she turned around. What fraction o

allsm [11]

We know that

[total trail]=(3/4)*2------> 6/4---------> (3/2) miles

[fraction of a mile that katenka did]=(2/3)*(3/2)------> 1 mile

the answer is 1 mile

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3 years ago

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kaheart [24]

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4 years ago