are both solutions for the homogeneous DE:The functions y1 =e" and y2 =ey"-16y = 0.Then, the general solution of nonhomogeneous DEy" – 16y = -32x – 16|isSelect one:O y= cje + ce - 2z +1Oy= Ce +cye - 2z - 1O y= ce" +cze +2z - 1O None of these.Oy= ce +cge +2z +1

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Answered: are both solutions for the homogeneous…

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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2. Which of the following is a general solution to the following: x²y" + xy' + (36x² - 1) y (Hint: As discussed in the lecture, use Y, only when J, and J-, are linearly dependent). A. y = c₁J₁(2x) + C₂J_1(2x) 6 B. y = C₁J₁(x) + C₂Y₁(x) 3 3 C. y = c₁₂/₁(6x) + C₂Y₁(6x) 0 D. y = c₁J₁(6x) + c₂] _1(6x) 2
check whether or not the given equations are homogeneous of some degree, and if yes, use an appropriate variable change to solve them
Let (a, b) =d. The linear Diophantine equation ax + by = c has a solution if and only if dc. Let xo, yo be any particular solution, that is, axo+byo = c. All other solutions are given by x = xo + (2) + t, y = Yo - (²) t where t is an arbitrary integer. (1.1)
The equations xy² + 4xzcos(u) + ye" = 8 and x yz + xe" – 6u?v² = 18 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (5,0). Find (u )zy at P. Türkçe: xy? + 4xzcos(u) + ye" = 8 ve x³ yz + xe" – 6u?v² = 18 denklemleri P noktası (x,y,z)=(1,1,1) ve (u, v) = (5,0) civarında x,y ve z'nin fonksiyonu olmak üzere u ve v için çözümlü olsun. P'de (u )y'yi hesaplayınız.) O 8,00 O 48,00 O - 0,25 O -20,00 O -60,00
2nd order linear homogenous DE with constant coefficients
eet - mgq-dwpo-stm J/0/c/MjUyNZAOMDAwMjl5/a/MJUOMZE1NZK3NTU1/details x + y = 6 x + y = "1 m = m = -2 b = b = SOLUTION: 2. y = 3x + 2 y - 3x = -1 -4 m = m = 4 5 b = b = SOLUTION: What does the graph of the equations look like for Problem 1? What does the graph of the equations look like for Problem 2? What do you notice about the slope of the lines? What do you notice about the y-intercept of the lines? What conclusion can you make from these equations and graphs? acer
For the equation ay" + by' + cy = 0, if b² – 4ac = 0 (the repeated root case where the root is r = -b/2a) we learned that one solution is Y1 = e-bt/2a, and the second linearly independent solution is y, = te-bt/2a We were told that the second solution is found via the Reduction of Order method. Apply the Reduction of Order method to the equation using the first solution (Do the calculations, this will take about 5 or so minutes) Which of the following equations does it reduces to? au" + 2bu' - u + cu = 0 2a 62 àu" – 2bu' +u + cu = 0 au" = 0 au" + 2bu' + Eu + cu = 0 O O O

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are both solutions for the homogeneous DE: The functions y1 =e" and y2 =e y" - 16y = 0. Then, the general solution of nonhomogeneous DE y" – 16y = -32z – 16 is Select one: O y= cje + ce -2z+1 Oy = e + cze – 2z – 1 Oy= ce + cge +2z - 1 O None of these. Oy= cje +ce + 2z +1