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 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. 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 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. 2ty (t) + 2y= 5+ 5t, y(1) = 7 y(t) =. where t>0

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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