4. The linear homogeneous differential equation with constant coefficientsy" -3y"-4y' +12y = 0 has an auxiliary equation whose roots are(C) -3,-4, 12(A) 2,-2,3(D) 1,-3,-4(B) 3,4,-12(E) -2,-7,8

Answered: Image /qna-images/answer/662106fd-1e9a-4673-b6a9-98b92b876483.jpg

Answered: 4. The linear homogeneous differential…

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

II. Rewrite the following second order differential equations as a system of first-order equations: (a) u" + 3u' +5u = 0 (b) u" + 6u' +9u = sin(2t)
Match the solution curve with one of the differential equations. O y" + 2y' + 2y = 0 O y" – 7y' + 12y = 0 О у" + 2y' +у %3D 0 О у" - 4y' - 5у %3D0 O y" + y = 0 O y" + 4y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) O The auxiliary equation should have one positive and one negative root, so that the solution has the form. + The differential equation should have the form y" + k?y = 0 where k = 1, so that the period of the solution is 2n. O The auxiliary equation should have two positive roots, so that the solution has the form c,ekı* + c,ek2*. O The auxiliary equation should have a repeated negative root, so that the solution has the form + O The differential equation should have the form y" + k?y = 0 where k = 2, so that the period of the solution is T. O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form eax(c, cos(Bx) + c, sin(Bx)).
Match the solution curve with one of the differential equations. y" + 4y = 0 О у" + 2y' + у %3D 0 O y" + y = 0 O y" – 2y' – 3y = 0 О у" - 7y' + 12у %3D 0 y" + 2y' + 2y = 0 Explain your reasoning. (Assume that k, k1, and k2 are all positive.) O The auxiliary equation should have a repeated negative root, so that the solution has the form cje-kx + c2xe¯kx. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form e"x(c1 cos Bx + c2 sin Bx). The differential equation should have the form y" + k?y = 0 where k = 1, so that the period of the solution is 2n. O The auxiliary equation should have one positive and one negative root, so that the solution has the form cqek1× + c2e¬k2×, The differential equation should have the form y" + k2y = 0 where k = 2, so that the period of the solution is n. O The auxiliary equation should have two positive roots, so that the solution has the form c1eki× + c2ek2×.
Which of the following systems could be used to obtain the solution to the differential equation y" - Sy" + Sy' - 2y = 0? (A) X = }3 (B) { = >2 (C) = y3 (D) = 2 - Sy- Sy2+ 2y3 (G) - y3 *= 1 *- Sy1 + 2y2 - Sys = 2y- Sy2 Sys - Sy - Sy2 + 2y3 y = 2y1 – Sy2 - 8ys (E) = 2 (F) - 3 (H) ý = 32 * = 91 *= 2y1 + 8y2- 5ys *= 2y1 - Sy2 - Sys = Sy1 + 2y2-Sy3
Find the solution of the following Differential Equations A) 4y" +7²y= 0, y(0) = 2, У (0) %3D0. B) y"+o²y=0, У(0) %3D А, У (0) %3 В. C) y" +2y' – 8 y = 0, y(0) = 1, У (0) %3 8.
Please help me with this question uploading for third time needed step by step solution with correct answer please... urgent
1. Find a system of first-order differential equations that correspond to the given second order differential equation: t²u" + 3tu' +u = t² + 2 Show all steps, including which new variables you are assigning to which terms.
1 - Find the values of (h,k) so that the differential equation dy (4x+3y–15) (2а+ у -7) substitution x = X + h, y =Y+k. | can be solved by using the dx а) (3, 2) b)(2, 3) с) (3, 1) d)(1, 3)

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

4. The linear homogeneous differential equation with constant coefficients y" -3y" - 4y' +12y = 0 has an auxiliary equation whose roots are (C) -3,-4, 12 (A) 2,-2,3 (D) 1,-3,-4 (B) 3,4,-12 (E) -2,-7,8