dy sin(y) - 4t with initial condition y(0) = 2 dt |3D Apply the forward Euler method with a step size of h = 0.3 to approximate the value of the function y(t) at t = 0.3 and t = 0.6. Your calculator should be in radians mode. Show your calculations.

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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Given linear 1st order ode
### Forward Euler Method Application

**Differential Equation:**

\[
\frac{dy}{dt} = \sin(y) - 4t
\]

**Initial Condition:**

\[
y(0) = 2
\]

**Task:**

Apply the forward Euler method with a step size of \( h = 0.3 \) to approximate the value of the function \( y(t) \) at \( t = 0.3 \) and \( t = 0.6 \). Your calculator should be in radians mode. 

**Instructions:**

Show your calculations systematically for each time step.
Transcribed Image Text:### Forward Euler Method Application **Differential Equation:** \[ \frac{dy}{dt} = \sin(y) - 4t \] **Initial Condition:** \[ y(0) = 2 \] **Task:** Apply the forward Euler method with a step size of \( h = 0.3 \) to approximate the value of the function \( y(t) \) at \( t = 0.3 \) and \( t = 0.6 \). Your calculator should be in radians mode. **Instructions:** Show your calculations systematically for each time step.
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