Mathematics

This is a linear first-order differential equation — the key is recognizing that $y$ and its derivative appear linearly, so you can use an integrating factor to collapse the left side into a derivative of a product. Find the integrating factor $\mu(x)$ from the coefficient of $y$, multiply through, and integrate both sides. The initial condition $y=0$ at $x=\frac{\pi}{2}$ then pins down the constant of integration to give you the particular solution.

This is a linear first-order differential equation — the key is recognizing that $y$ and its derivative appear linearly, so you can use an integrating factor to collapse the left side into a derivative of a product. Find the integrating factor $\mu(x)$ from the coefficient of $y$, multiply through, and integrate both sides. The initial condition $y=0$ at $x=\frac{\pi}{2}$ then pins down the constant of integration to give you the particular solution.