2. Consider the nonhomogeneous equation= a(t)y + b(t)and its associated homogeneous equationdy= a(t)y.dt(a)Prove that if y(t) is a solution of (3) and y,(t) is a particular solution of (2), then y(t) + y(t) isalso a solution of (2).(b)Prove that if yp, (t) and yp, (t) are two particular solutions of (2), then yp, (t)- yp2 (t) is a solutionof (3).dt

Answered: Image /qna-images/answer/48552e53-c434-4c74-8ee3-9ca9495e619e.jpg

2. Consider the nonhomogeneous equation = a(t)y+b(t) and its associated homogeneous equation a(t)y. dt (a) Prove that if y(t) is a solution of (3) and yp(t) is a particular solution of (2), then y(t) + Up (t) is also a solution of (2). Prove that if yp, (t) and yp, (t) are two particular solutions of (2), then yp, (t)- yp. (t) is a solution of (3). dt

2. Consider the nonhomogeneous equation = a(t)y+b(t) and its associated homogeneous equation a(t)y. dt (a) Prove that if y(t) is a solution of (3) and yp(t) is a particular solution of (2), then y(t) + Up (t) is also a solution of (2). Prove that if yp, (t) and yp, (t) are two particular solutions of (2), then yp, (t)- yp. (t) is a solution of (3). dt

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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