Please solve & show steps... **Problem Statement:**Find the solution of the given initial value problem in explicit form.\[\sin(2x) \, dx + \cos(9y) \, dy = 0, \quad y \left( \frac{\pi}{2} \right) = \frac{\pi}{9}\]**Solution:**\[y(x) = \text{[Solution here]}\]**Explanation:**This problem is asking to solve a differential equation with given initial conditions. 1. **Step 1: Separate Variables** - Rewrite the equation by separating variables involving \( x \) and \( y \). \[ \sin(2x) \, dx = -\cos(9y) \, dy \]2. **Step 2: Integrate Both Sides** - Integrate both sides of the equation. \[ \int \sin(2x) \, dx = -\int \cos(9y) \, dy \]3. **Step 3: Apply Initial Conditions** - After finding the integrals, apply the initial condition \( y \left( \frac{\pi}{2} \right) = \frac{\pi}{9} \) to determine the constant of integration.4. **Step 4: Solve for \( y(x) \)** - Express the equation in the explicit form \( y = y(x) \).The box is provided to input the final answer for \( y(x) \).

Name: Please solve & show steps... **Problem Statement:**Find the solution o
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Please solve & show steps... **Problem Statement:**Find the solution of the given initial value problem in explicit form.\[\sin(2x) \, dx + \cos(9y) \, dy = 0, \quad y \left( \frac{\pi}{2} \right) = \frac{\pi}{9}\]**Solution:**\[y(x) = \text{[Solutio