(MULTIPLE CHOICE) Which of the following statements is(are) true?(A) y = e3 is a solution of the DE y" – y – 12y = 0.(B) y" – by +5y = -9 In 2x is a nonhomogeneous linear DE which can be solved by undeterminedcoefficients.(C) The roots of the auxiliary equation of the DE " +5y + 6y = 0 are distinct imaginary.(D) The roots of the auxiliary equation of the DE y" + 3y" – 4y = 0 are both real and distinct.

Answered: Image /qna-images/answer/e0bfec7b-8327-4756-8761-1401ae4b8425.jpg

Answered: MULTIPLE CHOICE) Which of the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. (a) Rewrite t+ß using Euler's Formula. (b) Construct an example of a Cauchy-Euler equation whose characteristic equation has non- real roots. (c) Solve the equation you constructed in part (b) and use the formula from part (a) to rewrite the solution in terms of real valued functions.
2) Use guessing to find particular solutions to the following equations. b) y" - 2y' - 3y = 9t².
Advanced Math Question
(a) Give a real general solution to the equation(D2 + 8D + 41)^3 (D + 7)^2w = 0 : (b) Give a real general solution to the equationy'' - 36y = 8e^2t ; given that (-1/4e2t) is a solution to it.
Which of the following equations is not the DE of the solution correspond to y=C; e2x + C2 e4X + 2xe2x ? Select one: O y"+ 2y' - 8y = 4 e2× In e³x O y" + 2y' - 8y - 12e2x= 0 O y" + 2y' - 4(2y + 3e2x ) = 0 o y" + 2y' + 8y = 4(4y+3e?x ) O y" + 2y' + 8y = 12e2x + 8 In e²y
Determine the general solution of 2y" + 3y +y=t+e=t Hints: Undetermined coefficients and solve two nonhomogeneous equations: one with t and another one with et and then add the solutions.
Find a particular solution to the given equation. y"" - 6y" + 11y - 6y= e² (3 + 10x)
If a and ß are the roots of the equation x² – 3x + 4 = 0, the equation whose roots are a? + a + 1 and B² + B + 1 is (a) x' - 6x + 19 = 0 (b) х? + 6х - 37 %3D 0 (c) x' + 6x - 19 = 0 (d) x² - 6x + 37 = 0 If a, and B, are the roots of the equation 3x? - 2x – 5 = 0 and a, and B, are the roots of the equation 2x² + x - 7 = 0, the equation whose roots are (a,a, + B,B,) and (a,ß, + a,B,) is (a) 36x? – 12x + 911 = 0 (b) 9х* - 91х + 11 %3D0 (c) 36x? + 12x - 911 = 0 (d) 9x² + 91x – 19 = 0 3x-2 If a and B are the roots of the equation 7X- 3 5x 1 = 4, 1 is
Use the method of undetermined coefficients to find one solution of y" + 3 y – 3 y = (-1x² – 2 x + 5) e2x . y =
LYn+1 . You are monitoring the movement of a 2D alien. After months of analysis, you have come up with a the following equation- Xn+1 7 2] Yn Which means, if at nth minute, the 2D aliean is at point (1, 2), at n+ 1thminute, they will be at point (7 x 1+2× 2, –4 × 1+1× 2)cint (11, –2) If you diagonalize the matrix that's been mentioned above, it should look like this - a e 1 0 d -1 f] Let's say, at minute 0, the 2D alien is at point (1,1). Let point (X5, Y5) be its position at minute 5. 1(a) What is the value of X_5 and Y_5 ?
Consider the equation z13 = (-1+ i). Find the value of z which satisfies this equation and which has the second smallest positive argument 0,0 < 0 < 2n. Express your answer as z = re" where %3D r = and 0 =
Which of the following is a solution of the following equation valid near the origin for x>0? 2x2(1- х)у" - x(1+7x)у +у30 1 xn+1 y= X+ > 15 n=1 (2n+3)(2n+5) 1 2 (2n- 3)(2n- 5)xn+1 15 n =1 y= x + O (-1)"x"+1 (2n- 3)(2n- 5) 1 15 n =1 1 E (2n+ 3)(2n+ 5)x+1 15 n =1 y=x+

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