1. Consider the fourth-order boundary-value problem Ф"" (х) — а*ф(х) %3D 0 P(0) = p"(0) = P(1) = p"(1) = 0 where a > 0. Show that there is a non-trivial solution p (x) if and only if sin a = 0. Note: This boundary-value problem arises in modeling the vibrations of a beam that is simply supported. Hint: Write the general solution of p"'(x) – a*p(x) = 0 as P(x) — С, cosh aх + с, sinh aах + сз сos aх + сл sin aх

1. Consider the fourth-order boundary-value problem Ф"" (х) — аф(х) %3D 0 P(0) = p"(0) = P(1) = p"(1) = 0 where a > 0. Show that there is a non-trivial solution p (x) if and only if sin a = 0. Note: This boundary-value problem arises in modeling the vibrations of a beam that is simply supported. Hint: Write the general solution of p"'(x) – ap(x) = 0 as P(x) — С, cosh aх + с, sinh aах + сз сos aх + сл sin aх

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

5. The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, Y₂ ) is given by D = √(x₂ −x₁)² + ( Y₂ −Y₁ )² dD If x₁ = 4 cost, y₁=2 sint, x₂ =2 sin 2t and y₂ =3 cos 2t find when t = π dt
SOLVE STEP BY STEP IN DIGITAL FORMAT 3. Is the series 2n convergent or divergent? Hint: quotient criterion
Consider the graph of r(t) given below. y -4- -2- 0 _y=r(t) -N- 2 A) If g (t) = sin (37r(t)), find g′ (1). B) If h(t)=r(r(t)). 4 C) Find r' (2). [Select] find h' (3). [Select] D) Find r' (5). [Select] 6 g' [Select] t >
Find the general solution of the equation = y" - 4y + 3y = sin(x)e²*
1. Find an interval for which the following has an unique solution: (x-2)y"+3y = x, y(3) =2,y'(3) = 1
Consider the dierential equationy'' + 4y' + 29y = 7t^3e^(-2t) cos(5t) : The reasoning behind your answers should be made clear. A.1. The forcing has a characteristic form. Give its degree, characteristic, and multiplicity. A.2. Write down the Key Identity and its derivatives with respect to z up to the orderneeded for the Key Identity Evaluation method. (You do not need to evaluate these at the characteristic.) A.3. Write down the form for the particular solution needed to start the Undetermined Coefficients method. (You do not need to plug this form into the differential equation.) A.4. Use the Green Function method with initial time 0 to express a particular solution in terms of two denite integrals that do not have t in their integrands. (You do not need to evaluate these integrals.)
How to solve no.3 only pls
(1)If A = (xy², yz³, Find grad(divA)