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Q1.Solve the following IVP by mean of the Laplace transform P.D.E. u = a²uxx -∞0 < x < ∞0,0 < t <∞ I.C. u(x,0) = sinx, -∞ < x <∞

Q1.Solve the following IVP by mean of the Laplace transform P.D.E. u = a²uxx -∞0 < x < ∞0,0 < t <∞ I.C. u(x,0) = sinx, -∞ < x <∞

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 7CR: Determine whether each of the following statements is true or false, and explain why. A differential...
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Q1.Solve the following IVP by mean of the Laplace transform P.D.E. u a²uxx -00<X<0,0<t<o I.C. u(x,0) = sinx, -∞ < x <∞ Q2. Solve the Finite vibrating string described by the IBVP P.D.E. ut a²uxx = B.Cs. (u(0,t) = 0 lu(L, t) = 0 I.C. (u(x,0) = sin(¹) \u(x,0)= (EG)sin(E) Q3. Solve the simple concentration problem ,0<x<L, 0 < t <∞ ,0 < t <∞0 ,0 ≤x≤L P.D.E. xu+u = 0,00<x<∞, 0<t<∞ I.C. u(x,0) = cos x, -∞0 < x <∞ By Method of Characteristics.
Transcribed Image Text:Q1.Solve the following IVP by mean of the Laplace transform P.D.E. u a²uxx -00<X<0,0<t<o I.C. u(x,0) = sinx, -∞ < x <∞ Q2. Solve the Finite vibrating string described by the IBVP P.D.E. ut a²uxx = B.Cs. (u(0,t) = 0 lu(L, t) = 0 I.C. (u(x,0) = sin(¹) \u(x,0)= (EG)sin(E) Q3. Solve the simple concentration problem ,0<x<L, 0 < t <∞ ,0 < t <∞0 ,0 ≤x≤L P.D.E. xu+u = 0,00<x<∞, 0<t<∞ I.C. u(x,0) = cos x, -∞0 < x <∞ By Method of Characteristics.
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