help meno. 3 1. Determine the general solotion of the following equationy"-y-y+y=16xe2. Solve the following boundary value problemy"+8y'+17y'+10y= 34sinx+12cosx; (0) =1, y'(0) = -3, y'(0) =83. Acompression rod of lengthlis loaded by a sinusoidal force as shown in Figure. The bendingline of the bar then approximately satisfies the following differential equation of 4th order.EB" + Fy" = 0, sinory* + a*y = K, sin(x)(with a = F/EI, B = x/l and K, = 0,/EI). Where Fis the constant compressive force inthe direction of the rod axis and El is the rod's bending stiffiness, which is also constant. Sinceneither deflections nor moments can occur in the two boundary points, the followingboundary conditions apply to the bending line y = y(x):y(0) = y() =0 ; y'(0) = y)=0Determine the solution of this boundary value problem with the assumption that a + B.Roda(x) - 0o sinRod

Using the method of undetermined the coefficients for particular solution for nonhomogeneous part.

3. A compression rod of length l is loaded by a sinusoidal force as shown in Figure. The bending line of the bar then approximately satisfies the following differential equation of 4th order: Ely"+Fy"=Q sin y + a²y=K, sin(x) (with a =F/EI, B=/l and K, -Q/EI). Where F is the constant compressive force in the direction of the rod ads and El is the rod's bending stiffness, which is also constant. Since neither deflections nor moments can occur in the two boundary points, the following boundary conditions apply to the bending line y = y(x): (0) (0)=0; y(0) -(1)-0 Determine the solution of this boundary value problem with the assumption that a # B. yt or Rod in(4x) Q(x)-Qosin

3. A compression rod of length l is loaded by a sinusoidal force as shown in Figure. The bending line of the bar then approximately satisfies the following differential equation of 4th order: Ely"+Fy"=Q sin y + a²y=K, sin(x) (with a =F/EI, B=/l and K, -Q/EI). Where F is the constant compressive force in the direction of the rod ads and El is the rod's bending stiffness, which is also constant. Since neither deflections nor moments can occur in the two boundary points, the following boundary conditions apply to the bending line y = y(x): (0) (0)=0; y(0) -(1)-0 Determine the solution of this boundary value problem with the assumption that a # B. yt or Rod in(4x) Q(x)-Qosin

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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