4.1PRELIMINARY THEORY-LINEAR EQUATIONS129ven in21. fi(1) = 1 + x (1) = x, fs(x) =xinitialiven in22. fi(1) = e", fa(x) = e, fax) = sinh xIn Problems 23-30 verify that the given functions form afundamental set of solutions of the differential equation onthe indicated interval. Form the general solution.= O for23. y"-y'- 12y = 0; e, e, (-0, )lution.24. y" – 4y = 0; cosh 2x, sinh 2x, (–x, x)25. y" – 2y' + 5y = 0; e cos 2x, e* sin 2x, (-, ∞)26. 4y" – 4y' + y = 0; ev2, xe², (-x, x)27. xy" – 6xy' + 12y = 0; x,x*. (0. x)ion oflitions28. xy" + xy' + y = 0; cos(ln x), sin(In x), (0, ×)solu-29. x'y" + 6x²y" + 4xy' – 4y = 0; x, x *,x² In x, (0, *)se thisndary30. y + y" = 0; 1,x, cos x, sin x. (-*, x)4.1.3 NONHOMOGENEOUS EQUATIONS) areon ofitionsIn Problems 31-34 verify that the given two-parameter fam-ily of functions is the general solution of the nonhomoge-neous differential equation on the indicated interval.31. y-7y' + 10y 24e:y= ce+ Ce + be". (-%, *)y is aterval32. y" +y = sec x:an beV=q Cos x+c sin x +x sin x + (cos x) In(cos x),

Answered: Image /qna-images/answer/774211f5-8650-4180-86b1-985a31c0a633.jpg

Answered: 30. y+y" = 0; 1, x, cos x, sin x, (-x,…

Math

Advanced Math

30. y+y" = 0; 1, x, cos x, sin x, (-x, x)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

Q: y' + y tan x = sin 2x cos³ x y3 given x=0, y=1

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

Q: y = sin(x) at |0, 0, with four equally – spaced points

Q: y"+y = sin x, use Method I

A: Given that: y''+y=sinx

Q: Q3) find the derivative of each function: 1) y=x?sin*2x + x cos-3x 2) y? = (sin2x)* + (cos2x)* + 2xy…

Q: sin' xcos* x dx x cos

A: Perform integration

Q: Suppose y is a function of x. Find y' given csc-1y + xy = sec 1 y.

A: Given, csc-1y+xy=sec-1y

Q: Find y SX a) y = 3 sin (x² + 5x - 3) y' = c) y = sin" (6x) y'= b) xE5X+2 d) y = In (2x) Y₁ = Y y' =

Q: 21. y = sin xy

A: y= sin xydydx=ddxsin xy =cos xyddxxy =cos xyxdydx+yddxx =cos xyxdydx+y =x…

Q: Q3) find the derivative of each function: 1) y=x sin 2x +x cosx

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Q3) Find the derivatives of the following functions a) fy=cos u, u=2x+x/2 find dy/dx at point(0,2)…

A: i am solving 1st two question for last question repost.

Q: (cos y+ ycosx)dx + (sin x –xsin y)dy = o

Q: y" + y = sec x tan x

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: Find y^" when y=sin(ax)*cos(bx),a,b any real numbers. Find y" when y = sin(ax) · cos(bx), when a, b…

A: The given function is: y=sin(ax)cos(bx) So, y'=sin(ax)ddx(cos bx)+cos(bx)ddx(sin(ax))…

Q: e) ay +sina-l, (,a) Equation of tangent 2.

Q: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

Q: Find y': y = cot 0 sin 0 O sin² 0 1-tan²0 O1+sin² 0 cos³0 O-1-cos² e sin³0 3

Q: GeoGebrä Task 1: This rectangle has been decomposed along its diagonal. Recompose the two pieces to…

A: A rectangle is a closed quadrilateral with four sides and four angles. All the four angles of the…

Q: 7) | sec x. dx

A: Given: ∫ sec5x dx

Q: Determine order and degree * d'y d'y + cos dr? dr? 2 O 5 undefine- Not linear

A: The degree of a differential equation is the power of its highest derivatives.

Q: Differentiate:

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: y-y-coshx Ans.

Q: If f(x) = ƒ' (2) - 6 sin x + 12 cos x, then Help: Post to forum

A: See this solution in below.

Q: Sesch (sinhtx) sech4x

A: Given integral, ∫cschsinh4xsech4xdx To evaluate the value of the integral.

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

4.1
PRELIMINARY THEORY-LINEAR EQUATIONS
129
ven in
21. fi(1) = 1 + x (1) = x, fs(x) =x
initial
iven in
22. fi(1) = e", fa(x) = e, fax) = sinh x
In Problems 23-30 verify that the given functions form a
fundamental set of solutions of the differential equation on
the indicated interval. Form the general solution.
= O for
23. y"-y'- 12y = 0; e, e, (-0, )
lution.
24. y" – 4y = 0; cosh 2x, sinh 2x, (–x, x)
25. y" – 2y' + 5y = 0; e cos 2x, e* sin 2x, (-, ∞)
26. 4y" – 4y' + y = 0; ev2, xe², (-x, x)
27. xy" – 6xy' + 12y = 0; x,x*. (0. x)
ion of
litions
28. xy" + xy' + y = 0; cos(ln x), sin(In x), (0, ×)
solu-
29. x'y" + 6x²y" + 4xy' – 4y = 0; x, x *,x² In x, (0, *)
se this
ndary
30. y + y" = 0; 1,x, cos x, sin x. (-*, x)
4.1.3 NONHOMOGENEOUS EQUATIONS
) are
on of
itions
In Problems 31-34 verify that the given two-parameter fam-
ily of functions is the general solution of the nonhomoge-
neous differential equation on the indicated interval.
31. y-7y' + 10y 24e:
y= ce+ Ce + be". (-%, *)
y is a
terval
32. y" +y = sec x:
an be
V=q Cos x+c sin x +x sin x + (cos x) In(cos x),

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Integration$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Number 21
please answer fully on paper and make sure its correct please i keep getting different answers
Series Solution Method. In each of Problems 1 through 20, solve the given differential equation by means of a power series about the given point o. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution.
Q3) find the derivative of each function: Dy secx+ tanx)(secx-tanx) 2)y (sin) = 1-x'y 3) find y = u,u = (1+ tan
The second derivative of y = In(sec x) is a) . 1 tan x b) y' = tanx sec x c) y =secx · tan x d) y' = sec² x
5.) Find by implicit differentiation dy dx a.) x+y = y² +2 b.) 4xel+yer=7 c.) ycos(x)=x^²+y2
11
sin' 0 cos 0 d0
iii) integrate
tan (2t) Sind Ser y cln (te Jand x=ehai' et}