y = 3 cost – 2y, y(0) = 0 (a) Find approximate values of the solution of the given initial value problem at t = 0.1,0.2,0.3 and 0.4 using the Euler method with h = 0.1. NOTE: Round your answer to three decimal places. y(0.1) = y(0.2) = y(0.3) = y(0.4) = (d) Find the solution y = $(t) of the given problem and evaluate %3D $(t) at t = 0.1, 0.2,0.3 and 0.4. y(t) NOTE: Round your answer to four decimal places. y(0.1) = y(0.2) = y(0.3) = y(0.4) z
y = 3 cost – 2y, y(0) = 0 (a) Find approximate values of the solution of the given initial value problem at t = 0.1,0.2,0.3 and 0.4 using the Euler method with h = 0.1. NOTE: Round your answer to three decimal places. y(0.1) = y(0.2) = y(0.3) = y(0.4) = (d) Find the solution y = $(t) of the given problem and evaluate %3D $(t) at t = 0.1, 0.2,0.3 and 0.4. y(t) NOTE: Round your answer to four decimal places. y(0.1) = y(0.2) = y(0.3) = y(0.4) z
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Differential Equations Using Euler's Method
#### Problem Description
Given the differential equation:
\[ y' = 3 \cos t - 2y, \quad y(0) = 0 \]
We are asked to solve the following problems:
#### (a) Euler's Method Approximation
Find approximate values of the solution of the given initial value problem at \( t = 0.1, 0.2, 0.3 \) and \( 0.4 \) using the Euler method with \( h = 0.1 \).
**NOTE:** Round your answer to three decimal places.
**Values to find:**
- \( y(0.1) \approx \) _______
- \( y(0.2) \approx \) _______
- \( y(0.3) \approx \) _______
- \( y(0.4) \approx \) _______
#### (d) Exact Solution Evaluation
Find the solution \( y = \phi(t) \) of the given problem and evaluate \( \phi(t) \) at \( t = 0.1, 0.2, 0.3 \) and \( 0.4 \).
**NOTE:** Round your answer to four decimal places.
**Values to find:**
- \( y(t) = \) ______________
- \( y(0.1) \approx \) _______
- \( y(0.2) \approx \) _______
- \( y(0.3) \approx \) _______
- \( y(0.4) \approx \) _______](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56945fae-aeca-4f60-8c3d-a266c334f238%2Fb2a9ee9c-8f9f-48c8-8dff-b1797957674c%2Fjmyldpr_processed.png&w=3840&q=75)
Transcribed Image Text:### Differential Equations Using Euler's Method
#### Problem Description
Given the differential equation:
\[ y' = 3 \cos t - 2y, \quad y(0) = 0 \]
We are asked to solve the following problems:
#### (a) Euler's Method Approximation
Find approximate values of the solution of the given initial value problem at \( t = 0.1, 0.2, 0.3 \) and \( 0.4 \) using the Euler method with \( h = 0.1 \).
**NOTE:** Round your answer to three decimal places.
**Values to find:**
- \( y(0.1) \approx \) _______
- \( y(0.2) \approx \) _______
- \( y(0.3) \approx \) _______
- \( y(0.4) \approx \) _______
#### (d) Exact Solution Evaluation
Find the solution \( y = \phi(t) \) of the given problem and evaluate \( \phi(t) \) at \( t = 0.1, 0.2, 0.3 \) and \( 0.4 \).
**NOTE:** Round your answer to four decimal places.
**Values to find:**
- \( y(t) = \) ______________
- \( y(0.1) \approx \) _______
- \( y(0.2) \approx \) _______
- \( y(0.3) \approx \) _______
- \( y(0.4) \approx \) _______
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