- #1
Ashley1nOnly
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Posted
Homework Equations
Posted
The Attempt at a Solution
Posted
I just need the work to be checked.
Linear differential equation hwk check
- Thread starter Ashley1nOnly
- Start date
In summary, the conversation was about a user asking for their work to be checked on a differential equation problem. The expert advised them to always check their solution by substituting it into the equation.
Posted
Posted
Posted
I just need the work to be checked.
- #2
Ashley1nOnly
- 132
- 3
I integrated to get the last part.
- #3
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My only comments are:
1. Your title is misleading; this is not a linear DE
2. Your answer should be an equation with ##y## and ##t##.
3. I won't comment on the steps because of the impossibility of editing images.
1. Your title is misleading; this is not a linear DE
2. Your answer should be an equation with ##y## and ##t##.
3. I won't comment on the steps because of the impossibility of editing images.
- #4
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
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Ashley1nOnly said:
Ashley1nOnly said:
I almost always avoid looking at posted images, but I can offer useful advice. If you have a differential equation and a (supposed) solution, the standard operating principle you should always apply is to check the solution for yourself, by substituting it into the differential equation and seeing if it "works".
1. What is a linear differential equation?
A linear differential equation is an equation that involves a dependent variable and its derivatives, with the derivatives appearing in a linear fashion. In other words, the dependent variable and its derivatives are raised to the first power and are not multiplied together or divided by each other.
2. How do you check a linear differential equation?
To check a linear differential equation, you need to first determine if it is in standard form, which is dy/dx = f(x). Then, you can check if it satisfies the linearity property, meaning that the dependent variable and its derivatives appear in a linear fashion. Finally, you can verify that the equation is linear by substituting in values for the variables and solving for both sides to see if they are equal.
3. What is the process for solving a linear differential equation?
The process for solving a linear differential equation involves separating the variables, integrating both sides with respect to their respective variables, and then solving for the constant of integration. This will give you the general solution, which can be further simplified by applying initial conditions or boundary conditions.
4. Can a linear differential equation have multiple solutions?
Yes, a linear differential equation can have multiple solutions. This is because the general solution of a linear differential equation includes a constant of integration, and different values of this constant will result in different solutions. However, if initial conditions or boundary conditions are given, there will typically be only one unique solution that satisfies those conditions.
5. What are some real-life applications of linear differential equations?
Linear differential equations have many real-life applications in fields such as physics, engineering, economics, and biology. They can be used to model the growth of a population, the flow of electricity in a circuit, the motion of a pendulum, and many other natural phenomena.
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