Logarithmic Approach to Solving Differential Equations
You are given the differential equation \(\frac{dy}{dx} = \ln(y)\). Solve this differential equation in three parts: (a) Express the differential equation in separable form suitable for integration using logarithmic functions. (b) Integrate both sides to find the general solution of the differential equation. (c) Determine the particular solution that satisfies the initial condition \(y(1)=e\).