How Do You Solve the Differential Equation y = C(e^(-αt) - e^(-βt))?

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In summary, X, Y, and Z represent variables in equations that need to be solved, allowing us to find their values and understand mathematical phenomena. The process for solving equations involves identifying the type of equation, isolating the variable, and performing necessary calculations. To avoid common mistakes, it is important to apply operations to both sides of the equation and check the final answer for accuracy. Different methods, such as substitution or elimination, can be used to solve equations depending on the type and personal preference.
  • #1
larner
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Homework Statement


X--Y----Z, starting with X only


Homework Equations


y=C(e^-(alpha*t) -e-^beta*t)

C, alpha, beta constts SUCH THAT C >0 0<alpha <beta

show dy/dt= 0 imply t = 1/ (beta -alpha )*ln (beta/alpha)


The Attempt at a Solution



no idea!
 
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  • #2
Well, since it asks you to show that dy/dx= 0, have you differentiated
[tex]y= c(e^{-\alpha t}- e^{\beta t}[/tex]?

Set that derivative equal to 0 and solve for t.
 
  • #3
Thanx, I trying to differentiate. Bt now sorted out! cheers!
 

Related to How Do You Solve the Differential Equation y = C(e^(-αt) - e^(-βt))?

What are X, Y, and Z in these equations?

In this context, X, Y, and Z represent variables in the equations that need to be solved. These variables could represent any number, letter, or symbol depending on the specific equation being solved.

Why is it important to solve these equations?

Solving equations allows us to find the values of the variables, which can help us understand and analyze various mathematical or scientific phenomena. This can also be useful in solving real-world problems and making predictions.

What is the step-by-step process for solving these equations?

The step-by-step process for solving equations involves identifying the type of equation, applying the appropriate operations to both sides of the equation to isolate the variable, and then solving for the variable by performing the necessary calculations.

What are some common mistakes to avoid when solving equations?

Some common mistakes to avoid when solving equations include forgetting to perform the same operation on both sides of the equation, making calculation errors, and not checking the final answer for accuracy.

Can these equations be solved using different methods?

Yes, there are often multiple methods for solving equations, such as substitution, elimination, or graphing. The method used may vary depending on the type of equation and personal preference.

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