Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter 14.2, Problem 15E
To determine
The solution of the heat equation
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Chapter 14 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 14.1 - (a) Show that erf(t)=10ted. (b) Use part (a), the...Ch. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Use the third and fifth entries in Table 14.1.1 to...
Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - A string is stretched along the x-axis between (0,...Ch. 14.2 - Prob. 2ECh. 14.2 - The displacement of a semi-infinite elastic string...Ch. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - The displacement u(x, t) of a string that is...Ch. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - In Problems 1118 use the Laplace transform to...Ch. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Show that a solution of the boundary-value problem...Ch. 14.2 - Prob. 21ECh. 14.2 - If there is a heat transfer from the lateral...Ch. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 1-6 find the Fourier integral...Ch. 14.3 - In Problems 712 represent the given function by an...Ch. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - In Problems 1316 find the cosine and sine integral...Ch. 14.3 - In Problems 17 and 18 solve the given integral...Ch. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Prob. 20ECh. 14.4 - In Problems 1-21 and 24-26 use the Fourier...Ch. 14.4 - Prob. 2ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 7ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Discussion problems 27. (a) Suppose...Ch. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RE
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- 1. Deduce the continuous function whose Laplace Transform is 10 F(p) : P(p?+9) 2. Find p?-3P+10 (1) L'P+5)(p°+81)} (P+5)(p²+81), p-9 (p+1)(p-3), (ii) 9 (ii) L'P+6)*+64arrow_forward6. Use the Laplace transform to solve the following IVP. The table is on the next page. y" + 3y - 10y = 8(r) with y(0) = 0 and y'(0) = 0.arrow_forward6. Use the Laplace transform to solve the following IVP. The table is on the next page. y" + 3y - 10y = S(x) with y(0) = 0 and y'(0) = 0.arrow_forward
- Let a, b and c be real numbers. When we apply the Laplace transform to the initial value problem y" + ay' + by = e¢t y(0) ==1 , y'(0) =-2 If we obtain Y (s} then which of the following values (s+1)- have to be a, b and c? a) a= 1, b = 2 , c=3. b) a = 2, b= 1, c=3 c) a= 1, b= 1, c 3. d) a = 1, b= 1, c = 1 e) None of themarrow_forward1. If L{f(t)} = F(s) then L{f""(t)} is, A) s²F(s) sf (0) - f'(0) B) s²F(s)-sf'(0) - f (0) A) B) Statement I only Statement II only 2. Which of the following statements is/are true? I. The Laplace transform of y(V) is s4L(y) - s³y(0) - s²y' (0) - sy" (0) - y'" (0). II. When solved using Laplace transforms, a higher order linear ODE with constant coefficients with available initial conditions yields a general solution. C A) F(s) = B) F(s) = D) -s +3 1 + (s²2s1) s(s² - 2s-1) 1 s(s²2s1) C) D) s³ F(s) - s² f(0) - sf'(0) - f"(0) s³ F(s) - sf'(0) - f (0) 3. What is the Laplace transform of the differential equation and initial value conditions given below? y" - 2y' - y = 1; y(0) = -1; y'(0) = 1 Both statements None of the choices. C) F (s) D) F(s) C) D) = = s+1 (s²2s1) 1 (s²2s-1) 4. Which of the following initial value problem satisfy the given Laplace transform A) y" + y = 0; y(0) = 1; y'(0) = 0 B) y"+y=0; y(0) = 0; y'(0) = 1 + 1 s(s²2s1) L{f(t)} y" + y = 1; y(0) = 0; y'(0) = 0 y" + y = 1;…arrow_forward4/4/2021 Section 15.4 Ennanceu madiyimui Hu.. 5. Use the Chain Rule to find dw where w = sin 12x cos 4y, x = and y = t". dt dw %3D dx (Type an expression using x and y as the variables.) dx dt (Type an expression using t as the variable.) dw %3D dy (Type an expression using x and y as the variables.) dy dt (Type an expression using t as the variable.) dw %3D dt (Type an expression using t as the variable.) dQarrow_forward
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