Solve M(x,y) from N(x,y) and Equation Provided

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In summary, to solve for M(x,y) using N(x,y) and an equation, you first need to isolate M(x,y) on one side of the equation using algebraic operations. Then, you can plug in the value of N(x,y) and solve for M(x,y) using basic arithmetic. This process will depend on the specific equation provided and may have limitations or restrictions, such as needing both M(x,y) and N(x,y) in the equation and potentially encountering complex solutions.
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sapiental
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Homework Statement



is it possible to find M(x,y) if I know N(x,y) and the equation i need to solve is N(x,y)^M(x,y) - M(x,y)*e^N(x,y) = 0?

both are linear functions

thanks, this is part of a longer differential equation and the above equations is what I end up with. Just need some input please.

Thanks!
 
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  • #2
If M(x,y) is in terms of both x and y then I would say no, because you only have one equation and two unknowns
 

1. How do you solve for M(x,y) when you have N(x,y) and an equation provided?

To solve for M(x,y), you would first need to isolate M(x,y) on one side of the equation by using algebraic operations such as addition, subtraction, multiplication, or division. Once you have M(x,y) by itself, you can plug in the values of N(x,y) and solve for M(x,y) using basic arithmetic.

2. What are the steps to solving for M(x,y) in this situation?

The steps to solving for M(x,y) would depend on the specific equation provided, but generally, you would need to identify which variable represents M(x,y) and use algebraic operations to isolate it on one side of the equation. Then, you can plug in the values of N(x,y) and solve for M(x,y) using basic arithmetic.

3. Can you provide an example of solving for M(x,y) using N(x,y) and an equation?

Sure, let's say we have the equation 2x + 3y = 10 and we want to solve for M(x,y) when N(x,y) = 2. We can start by isolating M(x,y) on one side of the equation, so we would subtract 3y from both sides to get 2x = 10 - 3y. Then, we can divide both sides by 2 to get the final equation of x = 5 - (3/2)y. Now, we can plug in the value of N(x,y) = 2 and solve for M(x,y). So, M(x,y) = 5 - (3/2)(2) = 5 - 3 = 2.

4. Can you use any equation to solve for M(x,y) using N(x,y)?

No, you would need an equation that includes both M(x,y) and N(x,y) in order to solve for M(x,y) using N(x,y). If the equation only has one variable, then you would not be able to solve for two variables simultaneously.

5. Are there any limitations or restrictions when solving for M(x,y) using N(x,y) and an equation?

There might be limitations or restrictions depending on the specific equation provided. For example, if the equation has multiple variables and you are only given the value of one variable, then you would not be able to solve for M(x,y) as there would be multiple possible solutions. Additionally, some equations may have complex solutions that cannot be easily solved using basic arithmetic.

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