Solving Differential Equation: dy/dx=3y | Travis

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In summary, a differential equation is an equation involving an unknown function and its derivatives used to model changing relationships between variables. To solve it, techniques like separation of variables, substitution, or integration can be used depending on the type and initial conditions. The notation dy/dx represents the derivative of y with respect to x, indicating the rate of change at any point. A solution is correct if it satisfies the equation and initial conditions, and can be verified by graphing it. Real-life applications include population growth, heat transfer, fluid flow, and electrical circuits in fields like physics, engineering, and economics.
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TravisUHEng
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Find the set of all solutions of the following differential equation

dy/dx=3y

I've gotten this far

y'=3y

y'/y=3

I feel like I'm forgetting a fundamental integration identity like,

y=ln(y'/y) <-- Not sure that is even correct.

I'm not sure. The book says the solution is y=Ce^3x. It makes sense, I'm just stuck somewhere between start and finish.

Any help?

Thanks,
Travis
 
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Solved it. Thanks.
 

1. What is a differential equation?

A differential equation is an equation that involves an unknown function and its derivatives. It is used to model relationships between variables that are continuously changing over time or space.

2. How do I solve a differential equation?

To solve a differential equation, you need to use techniques such as separation of variables, substitution, or integration to find the function that satisfies the equation. The specific method will depend on the type of differential equation and the initial conditions given.

3. What is the meaning of dy/dx in a differential equation?

dy/dx is a notation that represents the derivative of the function y with respect to x. It indicates the rate of change of y with respect to x at any given point.

4. How do I know if a solution to a differential equation is correct?

A solution to a differential equation is correct if it satisfies the equation and any given initial conditions. You can also check your solution by graphing it and verifying that it matches the behavior of the given function.

5. What are some real-life applications of solving differential equations?

Differential equations are used to model many phenomena in physics, engineering, economics, and other fields. Some examples include population growth, heat transfer, fluid flow, and electrical circuits.

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