- #1
Sam Donovan
- 12
- 0
Homework Statement
dy/dx= 200-2y. y(0)=75
Homework Equations
The Attempt at a Solution
Do you move dx over and integrate.
Do you just integrate it 200y-y^2+c
andrewkirk said:This sort of problem is easily solved using separation of variables.
andrewkirk said:This sort of problem is easily solved using separation of variables.
No. This is completely wrong. I would strongly advise you to look at some examples of this technique in your textbook.Sam Donovan said:I'm having a little trouble with this. I move it so it becomes
##dy/dx=200-2y##
##dy=200dx-2ydx##
I think what you're suggesting is to solve the problem as follows:Sam Donovan said:Homework Statement
dy/dx= 200-2y. y(0)=75
The Attempt at a Solution
Do you move dx over and integrate.
Do you just integrate it 200y-y^2+c
A differential equation is a mathematical equation that describes how a variable changes over time. It involves derivatives, which represent the rate of change of the variable.
Finding the exact value of a differential equation allows us to understand the behavior of a system and make predictions about its future state. It is also essential in many areas of science, such as physics, engineering, and economics.
There are several methods for solving differential equations, including separation of variables, substitution, and using integrating factors. Which method to use depends on the type of differential equation and the initial conditions given.
No, not all differential equations can be solved exactly. Some equations are too complex to be solved using analytical methods, and numerical methods must be used instead. However, many commonly occurring differential equations can be solved exactly.
Finding the exact value of a differential equation has numerous applications in real-world situations. For example, it can be used to model population growth, predict the behavior of electrical circuits, and understand the motion of objects in space. In economics, it can be used to analyze supply and demand, and in engineering, it can be used to design bridges and buildings.