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prace
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http://album6.snapandshare.com/3936/45466/844588.jpg
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Can Separation of Variables Solve My Math Problems?
- Thread starter prace
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In summary, the conversation discusses the process of separating variables in a problem involving exponents. The solution involves using the properties of exponents to rewrite the equation and eliminate the need for taking the natural log of both sides. The conversation ends with gratitude for the help provided.
- #2
courtrigrad
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[tex] \frac{dy}{dx} = e^{3x} \times e^{2y} [/tex] So [tex] \int \frac{dy}{e^{2y}} = \int e^{3x} dx [/tex].
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- #3
prace
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but the original problem had e raised to the 3x + 2y. The only way I know to get rid of that is to take the natural log of both sides right? If you do that, you are left with ln (dy/dx) on the left side. How did you get rid of the natural log there?
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- #4
courtrigrad
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By the properties of exponents we know that [tex] e^{3x+2y} = e^{3x}\times e^{2y} [/tex]. So we can separate variables without taking the natural log of both sides. In general, [tex] a^{n+m} = a^{n}\times a^{m} [/tex]
- #5
prace
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oOh... 
I can't believe I didn't see that! sigh... it is those little things that get me all the time.
thank you so much for your help
I can't believe I didn't see that! sigh... it is those little things that get me all the time. thank you so much for your help
FAQ: Can Separation of Variables Solve My Math Problems?
What is separation of variables?
Separation of variables is a mathematical technique commonly used in solving differential equations. It involves separating a multi-variable equation into simpler equations that can each be solved independently.
When should I use separation of variables?
Separation of variables is typically used when solving partial differential equations, where the variables are not completely independent. It is also useful when solving certain ordinary differential equations, such as those with separable variables.
How do I separate the variables in an equation?
The specific method for separating variables depends on the equation itself. Generally, you will need to rearrange the equation to have all the terms with one variable on one side and all the terms with the other variable on the other side. This allows you to integrate each side separately.
What are the advantages of using separation of variables?
Separation of variables allows for the solution of complex differential equations by breaking them down into simpler equations that are easier to solve. It also provides a systematic approach to solving certain types of equations and can help in understanding the behavior of the solution.
Are there any limitations to using separation of variables?
While separation of variables is a powerful technique, it is not always applicable to all differential equations. It is most useful for linear equations, and may not work for non-linear equations or those with special boundary or initial conditions. Additionally, it may not always yield the most general solution to an equation.