16. y" + 9y = 2x²e3x + 5 %3D
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
please help for # 16 and 19
![3.5 Problems
In Problems 1 through 20, find a particular solution yp of the
given equation. In all these problems, primes denote deriva-
tives with respect to x.
1. y" + 16y
3. у" — у' — 6у — 2 sin 3x
5. y" + y' + y = sin?
7. у" — 4у 3 sinh x
9. y" + 2y' – 3y = 1+ xe*
10. у" + 9у %3D 2 cos 3x + 3 sin 3x
33. y" + 9y = sin 2x; y(0) = 1, y'(0) = 0
34. y" + y = cos x; y(0) = 1, y'(0) = –1
35. y" – 2y' + 2y = x + 1; y(0) = 3, y'(0) = 0
36. y(4) – 4y" = x²; y(0) = y'(0) = 1, y"(0) = y(3) (0) = -1
37. y(3) – 2y" + y' = 1 + xe*; y(0) = y'(0) = 0, y"(0) = 1
38. у" + 2y' + 2у
39. y(3) + y" = x +e-*; y(0) = 1, y'(0) = 0, y"(0) = 1
40. y(4) – y = 5; y(0) = y'(0) = y"(0) = y(3) (0) = 0
41. Find a particular solution of the equation
2. y" — у' — 2у — Зх + 4
4. 4y" + 4y' + y = 3xe*
6. 2y" + 4y' + 7y = x²
8. y" – 4y = cosh 2x
e 3x
,//
sin 3x; y(0) = 2, y'(0) = 0
,//
-
y(4) – y(3) – y" – y' – 2y = 8x°.
11. у(3) + 4у' 3 3х — 1
13. y" + 2y' + 5y = e* sin x
15. y(5) + 5y(4) – y = 17
12. у (3)
14. y(4) – 2y" + y = xe*
16. y" + 9y = 2x²e3x + 5
»(3)
+ y' = 2 – sin x
42. Find the solution of the initial value problem consisting
of the differential equation of Problem 41 and the initial
conditions
17. у" + у 3D sin x + xcos x
18. y(4) – 5y" + 4y = e* – xe2x
19. y(5) + 2y(3) + 2y" = 3x² – 1
20. y(3) – y = e* +7
y (0) = y'(0) = y"(0) = y(3) (0) = 0.
-
43. (а) Write
Зіх
cos 3x +i sin 3x
= (cos x +i sin x)3
= e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03106fa3-330c-422f-ad56-a6718a5c3a13%2F32b1af85-fb89-48b1-996c-84f3b23fadd5%2F79uqw9q_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)