Solve Diff Eqn Problem: Find Lamda for y=exp(Lamda x)

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In summary, a differential equation is a mathematical equation used to describe the change of a quantity over time or space. There are various methods for solving differential equations, including separation of variables and substitution. Lambda (λ) is a constant used in the general solution of differential equations and can be found by creating an equation with the given function and its derivative. The solution of a differential equation with lambda represents the general form of the solution and helps to understand its behavior and characteristics.
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Quadruple Bypass
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well I am confused on what the problem is saying:

"For what value(s) of the constant (lamda) will y = exp((lamda)x) be a solution of the given differential equation? If there are no such (lamda)'s, state that."

what the hell is y = exp? if exp is an exponent, would that, differentiated, be 0?

any help would be appreciated :)
 
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ah, just found out what it means. for some reason the book didnt say that e is written as exp in ch 1, but instead says so in ch 21. go figure
 

FAQ: Solve Diff Eqn Problem: Find Lamda for y=exp(Lamda x)

What is a differential equation?

A differential equation is a mathematical equation that describes how a quantity changes over time or space. It involves the derivative of a function and is commonly used to model various physical and natural phenomena.

How do you solve a differential equation?

There are various methods for solving differential equations, depending on the type and complexity of the equation. Some common techniques include separation of variables, substitution, and using the method of undetermined coefficients.

What is lambda in a differential equation?

Lambda (λ) is a constant that is often used in the general solution of differential equations. It represents the eigenvalue of the equation and can be used to determine the behavior of the solution.

How do you find lambda in a differential equation?

To find lambda in a differential equation, you can use the given function and its derivative to create an equation and solve for lambda. In the case of y=exp(λx), you can take the derivative of y with respect to x and equate it to λy, then solve for λ.

What does the solution of a differential equation with lambda represent?

The solution of a differential equation with lambda represents the general form of the solution, which can be used to find specific solutions for different initial conditions. It also helps to understand the behavior and characteristics of the solution over time or space.

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