Solve the initial value problem. (tan (4y) - 1)dx + [4x sec ² (4y) + -] dy = 0, y(0) = 1 wro The solution is x tan 4y + In|y|-k=0 (Type an equation using x and y as the variables. Type an implicit solution.)
Solve the initial value problem. (tan (4y) - 1)dx + [4x sec ² (4y) + -] dy = 0, y(0) = 1 wro The solution is x tan 4y + In|y|-k=0 (Type an equation using x and y as the variables. Type an implicit solution.)
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
![**Problem Statement:**
Solve the initial value problem.
\[
(\tan(4y) - 1)dx + \left(4x \sec^2(4y) + \frac{1}{y}\right) dy = 0, \quad y(0) = 1
\]
**Provided Solution:**
The solution is:
\[
x \tan 4y + \ln |y| - k = 0
\]
There is a note indicating that this solution is "wrong."
**Instruction:**
Type an equation using \(x\) and \(y\) as the variables. Type an implicit solution.
**Additional Notes:**
The problem requires solving a differential equation with given initial conditions. The provided solution marked "wrong" suggests there might be an error in the integration or substitution. Double-check calculations and substitutions before finalizing the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2F9e0e3ac9-e02d-4407-8191-482f1642640a%2Fp9npai9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the initial value problem.
\[
(\tan(4y) - 1)dx + \left(4x \sec^2(4y) + \frac{1}{y}\right) dy = 0, \quad y(0) = 1
\]
**Provided Solution:**
The solution is:
\[
x \tan 4y + \ln |y| - k = 0
\]
There is a note indicating that this solution is "wrong."
**Instruction:**
Type an equation using \(x\) and \(y\) as the variables. Type an implicit solution.
**Additional Notes:**
The problem requires solving a differential equation with given initial conditions. The provided solution marked "wrong" suggests there might be an error in the integration or substitution. Double-check calculations and substitutions before finalizing the solution.
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