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Advanced Engineering Mathematics
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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Please show all work. Only do question 10.
R 3 Second and Higher Order Linear Differential Equations 6 2. y - y'= 0; y(0) = 4, y'(0) = 1, y"(0) = 3 y₁ (t) = 1, y₂(t)=e', y3 (t) = e 3. y) + 4y"=0; y(0) = 0, y'(0) = -1, e y₁ (t) = 1, Y₂(t) = t₁ Y3 (t) = cos 2t, 4. y" + 2y" = 0; y(0) = 0, y'(0) = 3, y₁ (t) = 1, y₂(t)=t, y3(t) = e-2¹ 5. ty" + 3y" = 0, t> 0; Tatabas y₁ (t) = 1, y₂(t) =t, Joe lo y(2) = 1, y' (2) = -, y" (2) = 1 69,00 rogorod sopail sho y(-1) = 1, y'(-1) = -1, y"(-1) = -1 y(t) =ť² y(t) = t¹ 6. ty"" + ty" - y = 0, t < 0; y₁ (t) = 1, y₂ (t) = ln(-t), 603 304 y" (0) = -4, y" (0) = 8 y4 (t) = sin 2t y" (0) = -8 Exercises 11-15: Exercises 7-10: barts to an 102 Consider the given differential equation on the interval -∞ < t <∞. Assume that th members of a solution set satisfy the initial conditions. Do the solutions form a fund mental set? 7. y" + 2ty' + t²y = 0, y₁ (1) = 2, y(1) = -1, y₂ (1) = -4, y₂(1)=2 8. y" + ty = 0, y₁ (0) = 0, y₁ (0) = 2, y₂ (0) = -1, y2 (0) = 0 9. y" + (sint)y = 0, y₁ (0) = 1, y₁ (0) = -1, y(0) = 0, y₂ (0) = 0, y2(0) = 2, y3 (0) = 2, y3 (0) = -2, y(0) = 1 10. y" + e'y"+y = 0, y₁ (1) = 0, y₁ (1) = 1, y(1) = 1, y₂(1) = 1, y3 (1) = 0 y (1) = 0, y3 (1) = -1, y3 (1) = 0, y₂(0) = 0, y₂(1) = -¹,
Transcribed Image Text:R 3 Second and Higher Order Linear Differential Equations 6 2. y - y'= 0; y(0) = 4, y'(0) = 1, y"(0) = 3 y₁ (t) = 1, y₂(t)=e', y3 (t) = e 3. y) + 4y"=0; y(0) = 0, y'(0) = -1, e y₁ (t) = 1, Y₂(t) = t₁ Y3 (t) = cos 2t, 4. y" + 2y" = 0; y(0) = 0, y'(0) = 3, y₁ (t) = 1, y₂(t)=t, y3(t) = e-2¹ 5. ty" + 3y" = 0, t> 0; Tatabas y₁ (t) = 1, y₂(t) =t, Joe lo y(2) = 1, y' (2) = -, y" (2) = 1 69,00 rogorod sopail sho y(-1) = 1, y'(-1) = -1, y"(-1) = -1 y(t) =ť² y(t) = t¹ 6. ty"" + ty" - y = 0, t < 0; y₁ (t) = 1, y₂ (t) = ln(-t), 603 304 y" (0) = -4, y" (0) = 8 y4 (t) = sin 2t y" (0) = -8 Exercises 11-15: Exercises 7-10: barts to an 102 Consider the given differential equation on the interval -∞ < t <∞. Assume that th members of a solution set satisfy the initial conditions. Do the solutions form a fund mental set? 7. y" + 2ty' + t²y = 0, y₁ (1) = 2, y(1) = -1, y₂ (1) = -4, y₂(1)=2 8. y" + ty = 0, y₁ (0) = 0, y₁ (0) = 2, y₂ (0) = -1, y2 (0) = 0 9. y" + (sint)y = 0, y₁ (0) = 1, y₁ (0) = -1, y(0) = 0, y₂ (0) = 0, y2(0) = 2, y3 (0) = 2, y3 (0) = -2, y(0) = 1 10. y" + e'y"+y = 0, y₁ (1) = 0, y₁ (1) = 1, y(1) = 1, y₂(1) = 1, y3 (1) = 0 y (1) = 0, y3 (1) = -1, y3 (1) = 0, y₂(0) = 0, y₂(1) = -¹,
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