Find the solution to the initial value problemy′−e−t+5y=−5,   y(0)=−1.𝑦′−𝑒−𝑡+5𝑦=−5,   𝑦(0)=−1.

Question

Find the solution to the initial value problemy′−e−t+5y=−5,   y(0)=−1.𝑦′−𝑒−𝑡+5𝑦=−5,   𝑦(0)=−1.
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Solution 1

The given differential equation is a first order linear differential equation. The general form of such an equation is y′ + p(t)y = g(t). In this case, p(t) = 5 and g(t) = e^-t - 5.

Step 1: Find the integrating factor e^(∫p(t) dt) = e^(∫5 dt) = e^(5t).

Step 2: Multiply every term of the differenti Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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