Ordinary differential equations: Introduction
Additional conditions for a differential equation
A function that satisfies an ODE is a solution of the differential equation. The ODE alone does not completely determine the solution: additional condition are needed. When these conditions are all related to the state at a certain time (usually one takes ) then we call it an initial value problem. In case all additional conditions relate to the boundaries of an area (e.g., the endpoints of a time interval), we call it an endpoint problem or boundary value problem.
This is the differential equation of exponential growth with constant growth rate .
Thus the general solution is equal to Substituting the initial condition gives the equation This simplifies to The solution of the initial value problem is
Thus the general solution is equal to Substituting the initial condition gives the equation This simplifies to The solution of the initial value problem is
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