x dx y 2x dy 0 – (Solve differential equation)

By: Prof. Dr. Fazal Rehman | Last updated: November 30, 2024

[latex] \[ \textbf{Q1: Solve the differential equation:} \quad x \, dx + 2xy \, dy = 0 \] \[ \textbf{Solution:} \] \[ x \, dx = -2xy \, dy \] \[ \frac{dx}{dy} = -2y \] Now integrate both sides: \[ \int 1 \, dx = \int -2y \, dy \] \[ x = -y^2 + C \] Thus, the solution to the differential equation is: \[ x = -y^2 + C \]
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