Powers Johnston
06/02/2024 · Middle School
Q2- A- Find an integrating factor for the following equation: B- solve the equation and find the general answer: C- find the privet answer if \( y\left(\frac{\pi}{4}\right)=\pi \) \( 2+\left(\frac{x}{y}-\frac{\sin y}{\sqrt{y}}\right) y^{\prime}=0 \)
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The differential equation \(2 + \left(\frac{x}{y} - \frac{\sin y}{\sqrt{y}}\right) y' = 0\) is non-linear and requires complex manipulation to find an integrating factor. Solving the equation involves separating variables and integrating, which may not result in a simple closed-form solution. To find the specific solution satisfying the initial condition \(y\left(\frac{\pi}{4}\right) = \pi\), numerical methods may be necessary.
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