initial-value problem
[initial-value problem|initial-value problem] An initial-value problem involves finding a solution that satisfies both the differential equation and an initial condition.
Definition
initial-value problem An initial-value problem involves finding a solution that satisfies both the differential equation and an initial condition. The solution is determined by first identifying antiderivatives and then applying the initial value to select the specific antiderivative.
Effects
initial-value problem Solving the initial-value problem requires finding the function that satisfies both the differential equation and the initial condition. The problem involves determining the velocity function v(t) given v'(t) = -15 and v(0) = 88, while also addressing the related equation s'(t) = -15t + 85 with s(0) = 0.
Examples
initial-value problem Looking for a function y that satisfies the differential equation dy/dx = 6x and the initial condition y(0) = 5 exemplifies an initial-value problem.