# Autonomous Differential Equation

n.a.s.h

## Homework Statement

solve the following...

dy/dt= 0.5(100-y) with initial condition:y(0)=20

## The Attempt at a Solution

i found the general equation to be I=0.5Ln |100-y|+c
but im stuck as to what to do with the initial condition....

Mentor

## Homework Statement

solve the following...

dy/dt= 0.5(100-y) with initial condition:y(0)=20

## The Attempt at a Solution

i found the general equation to be I=0.5Ln |100-y|+c
but im stuck as to what to do with the initial condition....

What's "I"?

And you are saying that 0.5 * ln |100-y| + c is some kind of a solution to this DE?

$$\frac{dy}{dt} = \frac{100-y}{2}$$

n.a.s.h
yes i think its the general equation....

Science Advisor
Homework Helper
yes i think its the general equation....

I would say put t=0 and y=20 into that solution and then solve for the constant c, but I can't. Because there is no t. That's a problem. Can you show us how you got it? I think there's some other errors on the way.