kelvin2013 said:Homework Statement
Hi,
Just wondering if anyone knows how to solve the following as I am not sure where to start at all:
y''' + 8y = xsin(2x)
Any help would be great.
Homework Equations
The Attempt at a Solution
I'm thinking solving the homogeneous DE y'''+8y = 0 and then as far as I can see a possible solution maybe of the form yp=Axsin(2x)+Bxcos(2x)+Csin(2x)+Dcos(2x) ?
kelvin2013 said:Hi,
thanks for the reply - I get:
yp=c1e-2x+c2e(1+i√3)x+c3e(1-i√3)x
?
A third order differential equation is a mathematical equation that involves a function and its first, second, and third derivatives. It can be written in the form of y''' = f(x, y', y'', y''').
Third order differential equations can be complex and difficult to solve, especially when they involve real-life problems. Assistance with these equations can help to simplify and solve them more efficiently.
The most common methods used to solve third order differential equations are substitution, variation of parameters, and Laplace transforms. These methods involve manipulating the equation to reduce it to a simpler form that can be solved more easily.
It depends on the specific equation and the initial conditions given. Some third order differential equations can be solved analytically, while others may require numerical methods or approximation techniques to find a solution.
Third order differential equations are used in many scientific fields, including physics, engineering, and biology. They can be used to model and solve real-world problems involving motion, growth, and other dynamic processes.