Is y = sqrt(x-1) a Solution to 2yy' = 1?

In summary, the conversation discusses how to determine if the function y = φ(x) = sqrt ( x - 1 ) is a solution to the differential equation 2yy' = 1. It is explained that there is no need to rewrite the equation and the process of plugging y(x) into the equation to check if it holds. It is also mentioned that the original question may have been edited or changed.
  • #1
lap
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The question ask to determine whether y = φ(x) = sqrt ( x - 1 ) is a solution of the differential equation 2yy' = 1.
 
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  • #2
As far as "determine whether y = φ(x) = sqrt ( x - 1 ) is a solution of the differential equation 2yy' = 1" is concerned, there is no reason to "rewrite the equation". If y= sqrt(x- 1)= (x-1)^(1/2) then y'= (1/2)(x- 1)^(-1/2) so that 2yy'= 2(x- 1)^(1/2)[(1/2)(x- 1)^(-1/2)= what?

As for the rest, I don't see how that has anything to do with the problem. Are you sure you haven't looked up the solution to the wrong question?
 
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  • #3
Your wording is a bit confusing but if you're trying to determine if y(x) is a solution to your differential equation, all you have to do in plug y(x) into the equation and check if it holds.
 
  • #4
lap has edited his question and changed it completely. My first response was to a different question.
 

FAQ: Is y = sqrt(x-1) a Solution to 2yy' = 1?

What is a differential equation?

A differential equation is a mathematical equation that relates a function to its derivatives. It describes the relationship between a function and its rate of change.

What makes solving differential equation problems challenging?

One of the main challenges in solving differential equation problems is that the solutions are functions rather than numbers. Additionally, many differential equations do not have explicit solutions and require numerical or approximate methods of solving.

What are the different types of differential equations?

There are several types of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). These types differ in the number of variables and functions involved and the types of derivatives used.

How are differential equations used in science?

Differential equations are used in various scientific fields to model and understand natural phenomena. They are commonly used in physics, engineering, biology, economics, and many other fields to describe the behavior of systems and processes.

What are some common techniques for solving differential equations?

Some common techniques for solving differential equations include separation of variables, substitution, power series, and numerical methods such as Euler's method and Runge-Kutta methods. Each technique has its advantages and is suitable for different types of differential equations.

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