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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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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.
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.
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.
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.
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.