In other words, solve dy/dx = y/x as well as dy/dx = -y/x.rock.freak667 said:
Mark44 said:
The general solution of an ODE (ordinary differential equation) is a solution that includes all possible solutions to the equation, usually in the form of a function with one or more arbitrary constants. It is not specific to any initial or boundary conditions.
To obtain a general solution of an ODE, you need to integrate the equation with respect to the variable that the derivative is taken with respect to. This will result in a function with one or more arbitrary constants, which can then be solved for using initial or boundary conditions.
No, a general solution is not unique. It includes all possible solutions to the ODE, so there can be infinitely many general solutions for a single ODE. To obtain a unique solution, initial or boundary conditions must be specified.
A general solution includes all possible solutions to an ODE, while a particular solution is a specific solution that satisfies both the ODE and any specified initial or boundary conditions. A particular solution can be obtained by plugging in the specific values for the arbitrary constants in the general solution.
Yes, there are various methods for obtaining the general solution of an ODE, such as separation of variables, integrating factors, and substitution. The method used will depend on the specific form of the ODE. In some cases, it may not be possible to obtain a closed-form general solution and numerical methods may be used instead.