It is very difficult to understand what you mean. Do you mean that you are asked to find the general solution? And is "e^-2x- y" supposed to be "e^(-2x-y)" or "e^(-2x) - y"? Guessing at what you mean:intenzxboi said:the general solution for ye^x dy/dx = [e^-y ] + [ e^ -2x-y ]is:
so i tried to see if this was a homogenous equation but it is not.
next i tried to simplify and got:
y e^y dy= (1+e^-2x) dx / e^x
Differential equations are mathematical equations that involve an unknown function and its derivatives. They are used to model real-world situations and describe the relationship between a quantity and its rate of change.
Ordinary differential equations involve only one independent variable, while partial differential equations involve multiple independent variables. Ordinary differential equations are typically used to model single-variable systems, while partial differential equations are used for multi-variable systems.
Differential equations are used in many fields, including physics, engineering, economics, and biology. They can be used to describe the motion of objects, the spread of disease, the flow of fluids, and many other natural phenomena.
There are various methods for solving differential equations, depending on the type and complexity of the equation. Some common techniques include separation of variables, integrating factors, and using different types of substitutions.
While differential equations are powerful tools for modeling and understanding complex systems, they do have some limitations. They may not always have exact solutions, and numerical methods may be necessary to approximate solutions. Additionally, some systems may be too complex to accurately model with differential equations alone.