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thereddevils
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Homework Statement
Find the general equation of differential equation dy/dx=y+x
Homework Equations
The Attempt at a Solution
I don see a way to separate the variables. What substitution should i use?
Office_Shredder said:I only see three possible choices for a function in your equation: x, y, or x+y
thereddevils said:sorry but i don get what u meant
Office_Shredder said:I only see three possible choices for a function in your equation: x, y, or x+y
You said you were looking for a substitution! It wouldn't do much good to let u= x or u= y, would it? So what if u= x+ y?thereddevils said:sorry but i don get what u meant
thereddevils said:Homework Statement
Find the general equation of differential equation dy/dx=y+x
Homework Equations
The Attempt at a Solution
I don see a way to separate the variables. What substitution should i use?
A differential equation is a mathematical equation that relates the rates of change of a dependent variable to its independent variables. It describes how a quantity changes over time or in relation to other variables.
Differential equations are used in many scientific fields, such as physics, engineering, economics, and biology, to model and analyze various phenomena. They are also used to solve problems in areas like fluid dynamics, population growth, and electrical circuits.
The method for solving a differential equation depends on its type and complexity. Some common techniques include separation of variables, substitution, and using integral equations. Often, computer software is also used to numerically solve differential equations.
Ordinary differential equations involve only one independent variable, while partial differential equations involve multiple independent variables. Partial differential equations are commonly used to describe physical systems with multiple variables, such as temperature, pressure, and velocity.
Differential equations are important in science because they provide a powerful tool for understanding and predicting the behavior of complex systems. They allow scientists to model real-world phenomena and make predictions about future events. Many scientific laws and theories, such as Newton's laws of motion and the laws of thermodynamics, are expressed in the form of differential equations.