ideasrule said:Doesn't that simplify to y=-x?
What's your point? y' is a common factor in the equation you wrote. Did you not post the problem correctly?der.physika said:Did you consider the y' that it's not the same as y
You do realize we don't know what textbook you're using and even less likely to have a copy, right?der.physika said:Solve the Differential Equation [tex]2yy\prime+2xy\prime=0[/tex]
set [tex]p=y\prime[/tex], and then it becomes case 1 in the textbook
vela said:What's your point? y' is a common factor in the equation you wrote. Did you not post the problem correctly?
You do realize we don't know what textbook you're using and even less likely to have a copy, right?
Really? You don't see how x=-y is a solution to 2yy'+2xy'=2y'(x+y)=0?der.physika said:Okay, objection 1 makes no sense
vela said:Really? You don't see how x=-y is a solution to 2yy'+2xy'=2y'(x+y)=0?
vela said:You get that solution by canceling things out. It's not the only solution to the original equation, however.
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives, which represent the rate of change of a function, to model real-world phenomena.
There are several types of differential equations, including ordinary differential equations, partial differential equations, and stochastic differential equations. Ordinary differential equations involve a single independent variable, while partial differential equations involve multiple independent variables. Stochastic differential equations incorporate random variables into the equation.
Differential equations are used in various scientific fields, such as physics, engineering, biology, and economics, to model and analyze real-world phenomena. They can be used to understand and predict the behavior of systems and processes, such as population growth, chemical reactions, and fluid flow.
The order of a differential equation is determined by the highest derivative present in the equation. For example, a first-order differential equation contains only first derivatives, while a second-order differential equation contains second derivatives.
No, not all differential equations can be solved analytically. Some equations may not have a closed-form solution, meaning it cannot be written in terms of familiar mathematical functions. In these cases, numerical methods or approximations may be used to find a solution.