dy +(cos* r)y=1. dx 3 Solve cosa sin x
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
Diff Eqns
![**Problem Statement:**
Solve the differential equation:
\[
\cos^2 x \sin x \frac{dy}{dx} + (\cos^3 x) y = 1
\]
**Explanation:**
This is a first-order linear differential equation. The equation is given in the following format:
- The term \(\cos^2 x \sin x \frac{dy}{dx}\) represents the derivative of \(y\) with respect to \(x\), multiplied by \(\cos^2 x \sin x\).
- The expression \((\cos^3 x) y\) is a term involving the function \(y\), multiplied by \(\cos^3 x\).
- The equation is set equal to 1, indicating a non-homogeneous differential equation.
To solve, you'll typically isolate \(\frac{dy}{dx}\) and try to simplify or use an integrating factor.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78fa799e-dd0d-498f-bbc7-16121e7aabca%2Fb85b2117-0e29-4869-879b-415029f30d2b%2Fyh68htj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the differential equation:
\[
\cos^2 x \sin x \frac{dy}{dx} + (\cos^3 x) y = 1
\]
**Explanation:**
This is a first-order linear differential equation. The equation is given in the following format:
- The term \(\cos^2 x \sin x \frac{dy}{dx}\) represents the derivative of \(y\) with respect to \(x\), multiplied by \(\cos^2 x \sin x\).
- The expression \((\cos^3 x) y\) is a term involving the function \(y\), multiplied by \(\cos^3 x\).
- The equation is set equal to 1, indicating a non-homogeneous differential equation.
To solve, you'll typically isolate \(\frac{dy}{dx}\) and try to simplify or use an integrating factor.
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