Explanation Given information: y ' = g ( t , y ) = t 2 y where 0 ≤ t ≤ 1 with the initial condition y ( 0 ) = − 2 . Formula used: The endpoints ( t 0 , y 0 ) , ( t 1 , y 1 ) , ... , ( t n , y n ) of the line segments approximating the solution of the equation y ' = g ( t , y ) y ( a ) = y 0 on the interval a ≤ t ≤ b are given by the following formulas: t 0 = a , y 0 t 1 = t 0 + h , y 1 = y 0 + g ( t 0 , y 0 ) ⋅ h t 2 = t 1 + h , y 2 = y 1 + g ( t 1 , y 1 ) ⋅ h . t n = t n − 1 + h , y n = y n − 1 + g ( t n − 1 , y n − 1 ) ⋅ h Where, h = b − a n Calculation: Here, g ( t , y ) = t 2 y , a = 0 Ȁ

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications

15th Edition

ISBN: 9780137590469

Author: Larry Goldstein / David Lay

Publisher: Pearson Education (US)

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 10.7, Problem 5E

To determine

To calculate: The approximate solution f(t) to y'=t2y with the initial condition y(0)=−2 by using Euler’s method with number of iterations n=2 on the interval 0≤t≤1 and then find the value of f(1)

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.7, Problem 4E

Chapter 10.7, Problem 6E

Students have asked these similar questions

by Lagrange theorme find (4) Soultions independed for: 2x (y + z²) P + Y (29 +2²) q = 23

Help me with the accurate answer and solution asap pls pls thank yo u

Pls help me with accurate answer and solution as soon as possible pls thank you

Chapter 10 Solutions

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications

Ch. 10.1 - Show that any function of the form y=Aet3/3, where...Ch. 10.1 - If the function f(t) is a solution of the...Ch. 10.1 - Prob. 3CYU Ch. 10.1 - Show that the function f(t)=32et212 is a solution...Ch. 10.1 - Show that the function f(t)=t212 is a solution of...Ch. 10.1 - Show that the function f(t)=5e2t satisfies...Ch. 10.1 - Show that the function f(t)=(et+1)1 satisfies...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Is the constant function f(t)=3 a solution of the...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The approximate solution f ( t ) to y ' = t 2 y with the initial condition y ( 0 ) = − 2 by using Euler’s method with number of iterations n = 2 on the interval 0 ≤ t ≤ 1 and then find the value of f ( 1 )

Solution Summary: The author calculates the value of f(1) by using Euler’s method with number of iterations.

Concept explainers

Videos

To calculate: The approximate solution f(t) to y'=t2y with the initial condition y(0)=−2 by using Euler’s method with number of iterations n=2 on the interval 0≤t≤1 and then find the value of f(1)

Want to see the full answer?

Chapter 10 Solutions