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

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SUMMARY

The discussion centers on determining the value(s) of the constant λ for which the function y = exp(λx) serves as a solution to a specific differential equation. The confusion arises from the notation "exp," which represents the exponential function e raised to the power of λx. The participant clarifies that the book inconsistently uses "exp" in later chapters, leading to misunderstandings about its meaning in the context of differential equations.

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  • Understanding of differential equations
  • Familiarity with exponential functions
  • Knowledge of the constant e and its properties
  • Basic calculus, particularly differentiation
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  • Study the properties of exponential functions in differential equations
  • Learn how to solve first-order linear differential equations
  • Explore the relationship between λ and the solutions of differential equations
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Students and educators in mathematics, particularly those focusing on differential equations and exponential functions, as well as anyone seeking clarity on mathematical notation and terminology.

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
 

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