1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivahew [28]
3 years ago
10

Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Mathematics
1 answer:
Firdavs [7]3 years ago
6 0

Answer:

A) Particular solution:

2x+\frac{1}{2}e^{-x}-\frac{8}{5}

B) Homogeneous solution:

y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))

C) The most general solution is

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

Step-by-step explanation:

Given non homogeneous ODE is

y''+4y'+5y=10x+e^{-x}---(1)

To find homogeneous solution:

D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)

To find particular solution:

y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\

Substituting y_{p},y'_{p},y''_{p} in (1)

y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\

Equating the coefficients

5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\

The general solution is

y=y_{h}+y_{p}

from (2) ad (3)

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

You might be interested in
Alyssa took a math test with 30 questions, and she answered 24 questions correctly in order to get an a, she needs to answer at
koban [17]

Answer:

<u><em>No, she got an 80%</em></u>

Step-by-step explanation:

For every 3 questions she got right, that's 10%.

24/3= 8, which can be turned into 80%

So the answer is<u><em> no</em></u>.

6 0
3 years ago
The solution to 5x - 7 = 21?
lapo4ka [179]

Answer:

x = 5.6

Step-by-step explanation:

5x - 7 = 21

5x = 28

x = 5.6

Can I geet brainliest

4 0
3 years ago
Read 2 more answers
PLEASE I NEED HELP NOW!!! IF CORRECT I WILL GIVE BRAINLIEST!!
Ira Lisetskai [31]

Answer:

- 4 4/5 *C

Step-by-step explanation:

12:00-6:00 is 6hrs

7/10*6 = 42/10 = 4 1/5

1 - 4 1/5 = - 4 4/5

4 0
3 years ago
If a material absorbs almost all the light waves that reach it, what color will the human eye see?
Lisa [10]

Answer:

what

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Help pleaseee.......
Helga [31]

Answer:

i You to help yes You help me

5 0
3 years ago
Read 2 more answers
Other questions:
  • A vendor buys milk at a certain price, adds water and sells the adulterated milk at the same rate as he bought it for. He makes
    8·1 answer
  • Find The Number That Completes The Eqaution.
    12·2 answers
  • The product of nine and a number is added to 6, the result is 24. what is the number
    12·2 answers
  • Which linear equality will not have a shared solution set with the graphed linear inequality? y &gt;2/5 x + 2 y &lt;-5/2 x – 7 y
    6·2 answers
  • 29
    15·1 answer
  • What is the side length of a square with an area of 144x^2?
    12·1 answer
  • What is the measure of angle ABC of a circle
    14·1 answer
  • The equation 4s + 3d = 33 is used to determine the number of sandwiches, s, and drinks, d, that can be purchased with $33. If yo
    7·1 answer
  • Write each of the following expressions without using absolute value.
    9·1 answer
  • a triangle has sides with lengths of 33 centimeters, 75 centimeters, 89 centimeters. is it a right triangle?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!