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
labwork [276]
3 years ago
15

Find a particular solution to y" - y + y = 2 sin(3x)

Mathematics
1 answer:
leonid [27]3 years ago
8 0

Answer with explanation:

The given differential equation is

y" -y'+y=2 sin 3x------(1)

Let, y'=z

y"=z'

\frac{dy}{dx}=z\\\\d y=zdx\\\\y=z x

Substituting the value of , y, y' and y" in equation (1)

z'-z+zx=2 sin 3 x

z'+z(x-1)=2 sin 3 x-----------(1)

This is a type of linear differential equation.

Integrating factor

     =e^{\int (x-1) dx}\\\\=e^{\frac{x^2}{2}-x}

Multiplying both sides of equation (1) by integrating factor and integrating we get

\rightarrow z\times e^{\frac{x^2}{2}-x}=\int 2 sin 3 x \times e^{\frac{x^2}{2}-x} dx=I

I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx -\int \frac{2\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx-\frac{2I}{3}\\\\\frac{5I}{3}=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{5}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{5} dx

You might be interested in
Which of the following are like radicals? Check all of the boxes that apply
ElenaW [278]
There’s no answer choices to answer
8 0
3 years ago
3/4-(-7/6) Write your answer in simplest form.​
allsm [11]

Answer:

\frac{3}{4}  - ( -  \frac{7}{6} ) \\  =  \frac{3}{4}  +  \frac{7}{6}  \\  =  \frac{23}{12}  \\  = 1 \frac{11}{12}

6 0
3 years ago
A problem states: "There are 5 more girls than boys at the party. There are 27 children at the party in all. How many boys are t
Serhud [2]

Answer:

b + 5

Step-by-step explanation:

3 0
3 years ago
Delila earns $108.75 for working 15 hours as a holiday helper wrapping gifts. at this rate ,how much money will she earn if she
blsea [12.9K]
In 1 hour she earns $7.25
18 hours she earns $130.5
18 times 17.25 it’s $130.5
4 0
3 years ago
Read 2 more answers
Alex bought soccer shoes on sale
Radda [10]
He spent $34.50 in all
6 0
2 years ago
Read 2 more answers
Other questions:
  • Suppose M is the midpoint of line FG.
    8·1 answer
  • A local reading club has a set of 12 hardback books, a set of 8 paperback, And a set of 36 magazines each set can be divided amo
    5·2 answers
  • Please help promptly
    13·1 answer
  • Simplify -2x^3yxxy^2
    9·1 answer
  • (7)(-6)......simplify please
    8·1 answer
  • PLEASE HELP ASAP!<br> a. 4<br> b. 8<br> c. 16<br> d. 24<br> which one????
    15·2 answers
  • One number is four less than a second number. Four times the first is 14 more than 5 times the second. Find the numbers.
    10·1 answer
  • PLEASE HELP IN ATTACHED IMAGE
    5·2 answers
  • Which One Doesn't Belong (WODB)
    14·1 answer
  • A cone has height $h$ and a base with radius $r$ . You want to change the cone so its volume is doubled. What is the new height
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!