Or ##y = Ce^{-at} + \frac b a##xavier777 said:Question : General solution of dy/dt = -ay + b
My solution :
dy/dt = -a(y-b/a)
(dy/dt)/(y-(b/a)) = -a
Integrating both sides :
ln | y-(b/a) | = -at + C
e(-at+C) = y-(b/a)
Ce(-at) = y-(b/a)
Substitute your solution in the original differential equation and you should get a true statement.xavier777 said:How do I do that? Differentiate it to get back to the original diff eq ? If yes, then what about the assumption eCe-at = Ce-at ?
A general solution is a mathematical expression that satisfies a given equation or set of equations. It includes all the possible solutions to the equation, rather than a specific one.
A general solution can be checked by plugging it into the original equation. If it satisfies the equation, then it is considered a correct solution.
Yes, a general solution can be unique if the equation only has one solution or if the general solution is expressed in terms of a constant.
Finding a general solution allows for a better understanding of the behavior of a system or equation. It also provides a way to find specific solutions for different values of variables.
Yes, there are different methods for finding a general solution depending on the type of equation. Some common methods include separation of variables, substitution, and using specific formulas for certain types of equations.