Use the initial condition y(2) = 7 to determine the value of A that will satisfy the initial value problem. y = Ae* /2-x + 7 7 = Ae²²/2-2 +7 A = 2 y = 2 Substituting this value for A, solve the initial value problem. X
Use the initial condition y(2) = 7 to determine the value of A that will satisfy the initial value problem. y = Ae* /2-x + 7 7 = Ae²²/2-2 +7 A = 2 y = 2 Substituting this value for A, solve the initial value problem. X
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Using the Initial Condition to Solve for A**
To solve the initial value problem, use the initial condition \( y(2) = 7 \).
**Problem:**
The function is given by:
\[ y = Ae^{x^2/2 - x} + 7 \]
Substitute \( x = 2 \) into the equation using the initial condition:
\[ 7 = Ae^{2^2/2 - 2} + 7 \]
**Evaluating A:**
Attempted calculation for A:
There's an incorrect calculation for A shown as:
\[ A = \frac{2}{e^2} \]
**Substituting value for A:**
A box is provided where the final equation should be placed. However, the calculation and placement are marked with a red cross indicating an error.
\[ y = \]
The calculation needs to be reviewed to identify and correct the error in determining the value for A, ensuring it satisfies the initial condition provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe968be2-a1ee-4f2f-8a9b-67598232b5ea%2F8a39394a-27fa-4407-b1bd-06ca88f14022%2Fdyvbuvj_processed.png&w=3840&q=75)
Transcribed Image Text:**Using the Initial Condition to Solve for A**
To solve the initial value problem, use the initial condition \( y(2) = 7 \).
**Problem:**
The function is given by:
\[ y = Ae^{x^2/2 - x} + 7 \]
Substitute \( x = 2 \) into the equation using the initial condition:
\[ 7 = Ae^{2^2/2 - 2} + 7 \]
**Evaluating A:**
Attempted calculation for A:
There's an incorrect calculation for A shown as:
\[ A = \frac{2}{e^2} \]
**Substituting value for A:**
A box is provided where the final equation should be placed. However, the calculation and placement are marked with a red cross indicating an error.
\[ y = \]
The calculation needs to be reviewed to identify and correct the error in determining the value for A, ensuring it satisfies the initial condition provided.
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