Threads for solving differential equations by nature belong in the Calculus HW forum.fred_91 said:Homework Statement
Solve the differential equation:
dy/dx = 2/(x+e^y)
Hmm, this last equation is homogeneous, so setting v=ux should allow you to separate variables.fred_91 said:vv’-3v=-2x
Oh yes! This works very nicely.2nafish117 said:fred_91
hi
use this result to simplify it to a linear differential equation
dy/dx=1/(dx/dy)
A first order differential equation is an equation that involves a function and its derivative (or rate of change). It can be written in the form of dy/dx = f(x,y), where y is the function and x is the independent variable.
To solve a first order differential equation, you need to find an expression for y that satisfies the equation. This can be done by using various methods such as separation of variables, integrating factors, or variation of parameters.
An explicit solution expresses y as a function of x, while an implicit solution does not explicitly define y in terms of x. Instead, it involves an implicit relationship between x and y.
Yes, a first order differential equation can have infinitely many solutions. This is because the equation represents a family of curves, and each curve in the family is a solution.
Solving first order differential equations is a powerful tool in understanding and predicting the behavior of many natural phenomena such as population growth, chemical reactions, and electrical circuits. It is also used extensively in engineering, physics, and other scientific fields.