Solving a Separable Differential Equation with Interval Matching
Consider the differential equation defined piecewise: For \(x < a\): \(\frac{dy}{dx} = y\). For \(x \ge a\): \(\frac{dy}{dx} = -y\). Assume an initial condition \(y(x_0)=C\) for some \(x_0 < a\). (a) Solve the differential equation in each interval using separation of variables. (b) Determine the relationship between the integration constants by ensuring the solution is […]