Consider the following differential equation. t In(t)- dr + r = 4te² dt dr Find the coefficient function P(t) when the given differential equation is written in the standard form + P(t)r = f(t). dt P(t) = 1 tln(t) Find the integrating factor for the differential equation. (Do not include a constant of integration.) e/P(t) dt = x X Solve the given differential equation. sẻ to r(t) = In(t) X
Consider the following differential equation. t In(t)- dr + r = 4te² dt dr Find the coefficient function P(t) when the given differential equation is written in the standard form + P(t)r = f(t). dt P(t) = 1 tln(t) Find the integrating factor for the differential equation. (Do not include a constant of integration.) e/P(t) dt = x X Solve the given differential equation. sẻ to r(t) = In(t) X
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Consider the following differential equation:**
\[ t \ln(t) \frac{dr}{dt} + r = 4te^{t} \]
**Find the coefficient function \( P(t) \) when the given differential equation is written in the standard form:**
\[ \frac{dr}{dt} + P(t)r = f(t) \]
\[ P(t) = \boxed{\frac{1}{t \ln(t)}} \] ✔️
**Find the integrating factor for the differential equation. (Do not include a constant of integration.)**
\[ e^{\int P(t) \, dt} = \boxed{x} \] ❌
**Solve the given differential equation.**
\[ r(t) = \boxed{\frac{4e^{t} + c}{\ln(t)}} \] ❌](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a1305ef-606e-42df-8570-9f3784bb6037%2F51627171-c504-4dfc-aeb4-fc1d7647c0e5%2Fhpyrbc_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following differential equation:**
\[ t \ln(t) \frac{dr}{dt} + r = 4te^{t} \]
**Find the coefficient function \( P(t) \) when the given differential equation is written in the standard form:**
\[ \frac{dr}{dt} + P(t)r = f(t) \]
\[ P(t) = \boxed{\frac{1}{t \ln(t)}} \] ✔️
**Find the integrating factor for the differential equation. (Do not include a constant of integration.)**
\[ e^{\int P(t) \, dt} = \boxed{x} \] ❌
**Solve the given differential equation.**
\[ r(t) = \boxed{\frac{4e^{t} + c}{\ln(t)}} \] ❌
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