Let y(t) be the solution to y˙=5te^(-y)˙ satisfying y(0)=−3 (a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4),...,y(1.0) k t (base k) y(base k) 0 0 −3 1 0.2 ? 2 0.4 ? 3 0.6 ? 4 0.8 ? 5 1.0 ? (b) Use separation of variables to find y(t) exactly. y(t) = ? (c) Compute the error in the approximations to y(0.2),y(0.6), and y(1). |y(0.2)−y1|= ? |y(0.6)−y3|= ? |y(1)−y5|= ?
Let y(t) be the solution to y˙=5te^(-y)˙ satisfying y(0)=−3 (a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4),...,y(1.0) k t (base k) y(base k) 0 0 −3 1 0.2 ? 2 0.4 ? 3 0.6 ? 4 0.8 ? 5 1.0 ? (b) Use separation of variables to find y(t) exactly. y(t) = ? (c) Compute the error in the approximations to y(0.2),y(0.6), and y(1). |y(0.2)−y1|= ? |y(0.6)−y3|= ? |y(1)−y5|= ?
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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Question
Let y(t) be the solution to y˙=5te^(-y)˙ satisfying y(0)=−3
(a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4),...,y(1.0)
| k | t (base k) | y(base k) |
| 0 | 0 | −3 |
| 1 | 0.2 | ? |
| 2 | 0.4 | ? |
| 3 | 0.6 | ? |
| 4 | 0.8 | ? |
| 5 | 1.0 | ? |
(b) Use separation of variables to find y(t) exactly.
y(t) = ?
(c) Compute the error in the approximations to y(0.2),y(0.6), and y(1).
|y(0.2)−y1|= ?
|y(0.6)−y3|= ?
|y(1)−y5|= ?
Expert Solution
Step 1
Euler's method is a technique for numerical differentiation in which we compute the approximation
of the solution of a first order differential equation at a point using the given initial condition.
Comparing the given differential equation with , we have,
and with the step size .
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