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The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and 
= -1 is _________. (Answer up to three decimal places)
= -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer?
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Most Upvoted Answer
The solution (up to three decimal places) at x = 1 of the differentia...
Given D.E. is
∴ The auxiliary equation is:
(m + 1)2 = 0
⇒ m = -1, -1 [real and repeated]
The complementary function (C.F.):
yC = e-x[c1 + c2x]
And
∴ yp = 0 [particular integral]
∴ The complete solution of (1) is:
y = e-x[c1 + c2x]→(2)
Given that y(0) = 1
From (1) 1 = c1 + 0 ⇒ c1 = 1
dy/dx = -e-x[c1 + c2x] + e-x[c2]
Given: dy/dx = -1 at x = 0
-1 = -[1 + 0] + 1[c2] ⇒ c2 = 0
∴ y = e-x [1 + 0] = e-x ⇒ y(1) = e-1 = 0.368
II method:
Given D.E. is: 
⇒ y” + 2y’ + y = 0
Using L.T. on both sides:
L[y"] + 2L[y'] + L[y] = 0
⇒ s2L[y(x)] - sy(0) - y’(0) + 2[SL[y(x)]] - y(0) + L[y] = 0
⇒ (s2 + 2s + 1) L[y(x)] - s(1) - (-1) - 2(1) = 0
[∵ y(0) = 1 & y’(0) = -1]
⇒ (s2 + 2s + 1) L[y(x)] = 1 + s
Applying inverse L.T.
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The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and = -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer?
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The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and = -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and = -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and = -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer?.
The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and = -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and = -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution (up to three decimal places) at x = 1 of the differential equation d2y/dx2+2dy/dx + y = 0 subject to boundary conditions y(0) = 1 and = -1 is _________. (Answer up to three decimal places)Correct answer is '0.368'. Can you explain this answer?.
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