Solve the given equation.. dy dx a. + 2xy = x, y(0) = -2 C. y(x)= xex-2e-x² ex-5e-x² 2 b. y(x) = 1/2 y(x)=3-5e-x² 1-5e-x² y(x) = d. e. y(x) = 1-5ex
Solve the given equation.. dy dx a. + 2xy = x, y(0) = -2 C. y(x)= xex-2e-x² ex-5e-x² 2 b. y(x) = 1/2 y(x)=3-5e-x² 1-5e-x² y(x) = d. e. y(x) = 1-5ex
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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Question
![**Problem Statement:**
Solve the given differential equation:
\[
\frac{dy}{dx} + 2xy = x, \quad y(0) = -2
\]
**Options:**
a. \( y(x) = xe^x - 2e^{-x^2} \)
b. \( y(x) = \frac{e^x - 5e^{-x^2}}{2} \)
c. \( y(x) = \frac{1 - 5e^x}{2} \)
d. \( y(x) = 3 - 5e^{-x^2} \)
e. \( y(x) = \frac{1 - 5e^{-x^2}}{2} \)
**Note:**
- Ensure to check the solution with the initial condition \( y(0) = -2 \).
- Optionally, substitute the function back into the differential equation to verify if it satisfies both the equation and the initial condition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1300845a-828a-484d-8f06-319293900125%2F96627b9c-d83c-4f7f-b643-df061918e7a9%2Fyav5qqh_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the given differential equation:
\[
\frac{dy}{dx} + 2xy = x, \quad y(0) = -2
\]
**Options:**
a. \( y(x) = xe^x - 2e^{-x^2} \)
b. \( y(x) = \frac{e^x - 5e^{-x^2}}{2} \)
c. \( y(x) = \frac{1 - 5e^x}{2} \)
d. \( y(x) = 3 - 5e^{-x^2} \)
e. \( y(x) = \frac{1 - 5e^{-x^2}}{2} \)
**Note:**
- Ensure to check the solution with the initial condition \( y(0) = -2 \).
- Optionally, substitute the function back into the differential equation to verify if it satisfies both the equation and the initial condition.
Expert Solution
Step 1
The given equation is;
dy/dx+2xy=x, y(0)=-2.
Step by step
Solved in 3 steps with 2 images
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