- #1
delsoo said:dy/dx +Py(x) = Q(X) if i rearrange i would get 0.5 dy/dx + y/x = arc tan x ... is arc tan x function of x?
Integrate by parts. Do you remember how to take the derivative of arc tan x with respect to x?delsoo said:i redo the question and don't know how to proceed here... any idea on how should i do next ? i don't know how to integreate arc tan x
Yes. Let y = arc tan xdelsoo said:sorry , i checked thru the syllabus, there's no deriative of arc tan x in it or maybe i can do it in other way? any other way?
A differential equation is a mathematical equation that relates a function with its derivatives. It is used to model various physical or natural processes in the form of a mathematical equation.
A general solution of a differential equation is a set of solutions that satisfies the given differential equation. It includes all possible solutions that can be obtained by varying the constants in the solution equation.
To express y in terms of x for a general solution of a differential equation, you need to solve the differential equation by integrating both sides and then substitute the initial conditions to obtain the final solution.
Yes, a general solution of a differential equation can have multiple solutions. This is because it includes all possible solutions that satisfy the given differential equation, and each solution can have different values for the constants.
A general solution of a differential equation includes all possible solutions that satisfy the given differential equation, whereas a particular solution is a specific solution that satisfies the differential equation with given initial conditions. In other words, a general solution contains a set of solutions, while a particular solution is a single solution.