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Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved by defining the integrating factor p(t) =e a(1) dt and then multiplying both sides of the equation by p(t). The equation becomes p(t) (y'(t) + a(t)y(t)) = (P(t)y(t)) = p(t)f(t). To obtain the solution, integrate both sides with respect to t. Use this method to solve the following. Begin by computing the integrating factor. y'() +y() = 0. y(1) =3 What is the integrating factor? p(t) =|

Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved by defining the integrating factor p(t) =e a(1) dt and then multiplying both sides of the equation by p(t). The equation becomes p(t) (y'(t) + a(t)y(t)) = (P(t)y(t)) = p(t)f(t). To obtain the solution, integrate both sides with respect to t. Use this method to solve the following. Begin by computing the integrating factor. y'() +y() = 0. y(1) =3 What is the integrating factor? p(t) =|

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Sam Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved by defining the integrating factor p(t) = e a(t) dt and then multiplying both sides of the equation by p(t). The equation becomes p(t) (y'(1) + a(t)y(t)) d. (P(t)y(1)) = p(t)f(t). To obtain the solution, the form a = %3D dt integrate both sides with respect to t. Use this method to solve the following. Begin by computing the integrating factor. 6. y'(t) +y(t) = 0, y(1) = 3 What is the integrating factor? p(t) = |
Transcribed Image Text:Sam Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved by defining the integrating factor p(t) = e a(t) dt and then multiplying both sides of the equation by p(t). The equation becomes p(t) (y'(1) + a(t)y(t)) d. (P(t)y(1)) = p(t)f(t). To obtain the solution, the form a = %3D dt integrate both sides with respect to t. Use this method to solve the following. Begin by computing the integrating factor. 6. y'(t) +y(t) = 0, y(1) = 3 What is the integrating factor? p(t) = |
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