Theorem 3.1.1 Existence of a Unique SolutionLet añ(x), an−1(x), . . .‚ α₁(x), a(x), and g(x) be continuous on an interval I, and let a„(x) ‡ 0for every x in this interval. If x xo is any point in this interval, then a solution y(x) of theinitial-value problem (1) exists on the interval and is unique.= (a) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has aunique solution.(x+2) y'"' + (x² − 64) y″ + 14y = - = 4, y(0) = 0, y'(0) = 8, y″(0) = 8X-(b) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has aunique solution.1(x − 2) y'"' + (x² − 64) y″ + 14y = -¹4; _y(0)= 0, y'(0) = 8, y″(0) = 8X-|(A) (−4,−2) (B) (−2, ∞) (C) (2, ∞) (D) (-∞, -4) (E) (-∞, 4) (F) (-4,2) (G) (2,4) (H) (4, ∞) (I) (−4, ∞0)|(J) (−2, 4) (K) (-∞, 2) (L) (-∞, -2)|(A) (−4, 2)(B) (2,4) (C) (-∞,−4) (D) (2, ∞) (E) (-4, ∞) (F) (-4,-2) (G) (-∞, 4) (H) (-∞, −2) (I) (4, ∞)|(J) (−2, ∞) (K) (-∞, 2) (L) (−2, 4)

Answered: Image /qna-images/answer/3caa818a-3189-466f-91be-3bfbe057f4ab.jpg

Answered: (a) Find the largest interval on which…

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

Similar questions

We consider the initial value problem 9z?y" + 9zy' + y= 0, y(1) = 3, y'(1) = 2 By looking for solutions in the form y = z' in an Euler-Cauchy problem Az'y" +Bry' + Cy= 0, we obtain a auxiliary equation Ar? + (B – A)r +C =0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y1,Y2: (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is ye = C1y1 + c2y2. Find the unique solution satisfying y(1) = 3, y'(1) = 2 y =
7. (a) Use Euler's method to obtain y(0.6) to 4 decimal places for the DE y' = xy + √√y with the initial condition y(0) = 3. Use h=0.2. Show HOW the Euler's formula used to fill in the table below. Step 0 1 2 3 Xn 0 0.2 0.4 0.6 Yn 3 (b) Use the nspire calculator to find y(0.6) with an h of 0.05. Does your answer match with the true solution y(0.6)? Comment.
3. (a) Consider the DE 9y"-6y+y=0. Show how to find a solution y, to the DE (b) Demonstrate how to use the reduction of order formula (showing all integration and work) can be used to find a second solution and state the general solution to the DE.
Use (1) in Section 6.4. x²y" + xy' + (x² − v²)y = 0 (1) Find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.) x²y" + xy' + (x² - 49)y = 0 C₁J7(x) + C₂17(x) C₁J7(x) + C₂Y7(x) C₁J7(x) + C₂J_7(x) C₁J7(x) + C₂Y_7(x) O C₁J_7(x) + C₂1₂(x) Need Help? Submit Answer Read It Watch It
1. Find the solution of the given initial value problem. y’’+y=0, y(π/3)=2, y’(π/3)=-4 topic: complex roots of the characteristic equation.
We consider the initial value problem z?y" + 6zy' + 6y = 0, y(1) =1, y'(1) = -1 By looking for solutions in the form y = r" in an Euler-Cauchy problem Ar?y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar? + (B – A)r +C= 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y1, y2 (enter your results as a comma separated list ) (4) Recall that the complementary solution (i.e., the general solution) is ye = C1y1 + c2y2. Find the unique solution satisfying y(1) = 1, y'(1) = -1 y =
Consider the initial value problem: y" - y" - y' +y = -e*(4 – 8t), y(0) = 2, y'(0) = 0, y"(0) = 0 The real numbers a, b and e such that y(t) = (a + bt)e" + (c + t + t²)e™* is the exact solution of the IVP are: a= 2, b= -1, c= 1 O a=1, b= -1, c= 1 O a=0, b= 1, c= -1 a=2, b= -2, c= 1
We consider the initial value problem 18z?y" – 21zy' + 6y = 0, y(1) = 2, y'(1) = -2 By looking for solutions in the form y = z' in an Euler-Cauchy problem Az'y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar2 +(B – A)r + C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list ) (3) Find a fundamental set of solutions y1, 42 (enter your results as a comma separated list ) (4) Recall that the complementary solution (i.e., the general solution) is yc = C1y1 + c2y2. Find the unique solution satisfying y(1) = 2, y'(1) = -2

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS