Solve the wave equation a² 0¯uəx?a?u0 < x < L, t > 0 (see (1) in Section 12.4) subject to the given conditions.1.u(0, t) = 0, u(L, t) = 010hx0 <х<2neatu(x, 0) := 0100(1-2) 늘 도 x<10h 1< x < Lt = 0Σu(x, t) =+%Dn = 1

Answered: alu Solve the wave equation a². 0 < x <…

Calculus: Early Transcendentals

8th Edition

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Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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B\ Suppose that = 4 cos² t , x = d²y =- V3 sin(2t) and 0
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Exercise 4: In this problem, we solve the general case of sec" (x) dx. Note we know the cases n = 1, 2, 3, so we may as well assume n > 3 if this helps. (a) First, suppose n is even. Re-write sec" (x) = sec"-2 (x) · sec2 (x), use the Pythagorean theorem, and a u-substitution of u = tan(x) to solve the integral, similar to our previous methods. (b) Now, suppose n is odd. Use integration by parts in a very similar manner to the sec3 (x) case done in class to show the following: | sec" (x) dx sec"-2 (x) tan(x) – (n – 2) | sec"-2(x) tan² (x) dx. п-2 Conclude that: sec" (2) da = (see"- (r) tan(2) + (n – 2) 2(x) tan(x) + (n – 2) sec dx and hence we are done by induction.
part b please
Solve the wave equation 1 8Pu Uz(0, t) = u#(1, t) = 0 4 dx2* Pu u(x, 0) = x(1– x), Ut(x, 0) = sin(3Tx).
4 (4 + 3)² dt S cos t dt 1 + sin t sec x tan x dx 1 sec x
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A string with motionless ends at x = 0 and x = 1 vibrates according to the wave equation Fu Ət² and the initial velocity J²u dr² 1. Use separation of variables (show details) to solve the equation provided that the initial profile of the string is u(x,0) = 4 sin(2x) Ju 5- Ət It=0 = 0.
+) Solve Poisson problem for a=lı bal ру u(x₁b) = f₂(x) Du= f(x,y) u(0₁9)=9₁ (9) b 0 u(a.y) = 9₂ (y) >x a u(x₁) = f(x) Figure 1. f(x,y) = sin2TX₁ f₁ = £₂=0, 9₁=9₂=0 using one dimensional eigen function expansion.

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alu Solve the wave equation a². 0 < x < L, t > 0 (see (1) in Section 12.4) subject to the given conditions. at? u(0, t) = 0, u(L, t) = 0 10hx 0 < x < 5 du u(x, 0) = = 0 |10(3 - 4). at < x < L t = 0 u(x, t) = Σ n = 1