In exercises 1-10, classify each of the following integral equations as Fredholm orVolterra integral equation, linear or nonlinear, and homogeneous or nonhomogeneous:(1) u(x) = x +(2) u(x) = 1 + x² + √(x − t)u(t) dt-(3) u(x) = e² + ² tu²³ (t) dt3(6) u(x) = ²So(4) u(x) = f (x - t)² u(t) dt(5) u(x) = ²/2 + (¹xtu(t) dt(7) u(x) = 1 +xtu(t) dt(10) u(x) =1x+ 5+x3 6(x-1)³ u(t) dt1= 1-1x+tu(t)/0(8) u(x) = = = cos x + ²/2 √² cos x u(t) dt[²* (x − 1)² u² (1) dt(9) u(x) = 1 +10dt- 5²(x - t)u(t) dt

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Answered: In exercises 1-10, classify each of the…

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.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 12CR

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Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.
A special class of first-order linear equations have the form a(t)y'(t) + a'(t)y(t) = f(t), where a and f are given functions of t. Notice that the left side of d. this equation can be written as the derivative of a product, so the equation has the form (a(t)y(t)) = a(t)y'(t) + a'(t)y(t) = f(t). Therefore, the equation can be solved by integrating both sides with respect to t. Use this idea to solve the following. he form 2ty'(t) + 2y = 5 + 5t, y(1) = 7 y(t) = where t> 0
A special class of first-order linear equations have the form a(t)y'(t) + a'(t)y(t) = f(t), where a and f are given functions of t. Notice that the left side of d. this equation can be written as the derivative of a product, so the equation has the form (a(t)y(t)) = a(t)y'(t) +a'(t)y(t) = f(t). Therefore, the dt equation can be solved by integrating both sides with respect to t. Use this idea to solve the following. s the form 4+3t Fy() + 5t*y = y(1) = 4 %3D y(t) = |, where t>0
A special class of first-order linear equations have the form a(t)y'(t) + a'(t)y(t) = f(t), where a and f are given functions oft. Notice that the left side of d this equation can be written as the derivative of a product, so the equation has the form (a(t)y(t)) = a(t)y'(t) + a'(t)y(t) = f(t). Therefore, the dt equation can be solved by integrating both sides with respect to t. Use this idea to solve the following. the form e -ly'(1) – e -ly= e 51. y(0) = 4 y(t) =
which is the solution vector x(t)=(x(t)) of differential equation system (y(t))
which is the solution vector x(t)=(x(t))of differential equation system (y(t))
A special class of first-order linear equations have the form a(t)y'(t) + a'(t)y(t) = f(t), where a and fare given functions of t. Notice that the left side of this equation can be written as the derivative of a product, so the equation d has the form (a(t)y(t)) = a(t)y' (t) + a'(t)y(t) = f(t). Therefore, the equation can be solved by integrating both sides with respect to t. Use this idea to solve the following. 2ty' (t) + 2y = 3 + 2t, y(1) = 7
find the linearization at x = a. f (x) = x4, a = 1
Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(r) = cos² r are linearly independent on the interval (-x, 0).
Find a linear differential operator that annihilate the given function a) y=7e2x b) y=x+3xe6x

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