a special class of first order linear equations have the form atlyt tjyt ft where and are given

Name: a special class of first order linear equations have the form atlyt tjyt ft where and are given functions of notice that the left side of this equation can be written as the derivative of pr 72369
Uploaded: 2023-02-18T13:42:06-08:00
Duration: 2 min 54 s
Channel: Sri K
Description: a special class of first order linear equations have the form atlyt tjyt ft where and are given functions of notice that the left side of this equation can be written as the derivative of pr 72369

Question

A special class of first-order linear equations has the form a(t)y'(t) + b(t)y(t) = f(t), where a(t) and b(t) 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) = f(t). Therefore, the equation can be solved by integrating both sides with respect to t. Use this idea to solve the following: 8y'(t) + 6y(t) + 5y(t) = f(t) y(1) = 9 y(t)

          A special class of first-order linear equations has the form a(t)y'(t) + b(t)y(t) = f(t), where a(t) and b(t) 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) = f(t). Therefore, the equation can be solved by integrating both sides with respect to t. Use this idea to solve the following:
8y'(t) + 6y(t) + 5y(t) = f(t)
y(1) = 9
y(t)

Added by Debbie B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/18/2023

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A special class of first-order linear equations has the form a(t)y'(t) + b(t)y(t) = f(t), where a(t) and b(t) 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) = f(t). Therefore, the equation can be solved by integrating both sides with respect to t. Use this idea to solve the following: 8y'(t) + 6y(t) + 5y(t) = f(t) y(1) = 9 y(t)