n.a.s.h said:Homework Statement
solve the following...
dy/dt= 0.5(100-y) with initial condition:y(0)=20
Homework Equations
The Attempt at a Solution
i found the general equation to be I=0.5Ln |100-y|+c
but I am stuck as to what to do with the initial condition...
n.a.s.h said:yes i think its the general equation...
An autonomous differential equation is a type of differential equation where the independent variable does not appear explicitly. This means that the rate of change of the dependent variable is only dependent on the value of the dependent variable itself.
In a non-autonomous differential equation, the independent variable is explicitly present in the equation and affects the rate of change of the dependent variable. In contrast, an autonomous differential equation does not have this dependence on the independent variable.
Autonomous differential equations are used to model various natural phenomena such as population growth, chemical reactions, and electrical circuits. They are also commonly used in physics, engineering, and economics.
Autonomous differential equations are typically solved using analytical or numerical methods. Analytical methods involve finding the exact solution using mathematical techniques, while numerical methods use approximations to find an approximate solution.
Autonomous differential equations are advantageous because they can provide a simplified and general representation of complex systems. They can also be used to make predictions and understand the behavior of a system over time.