I don't know what you mean by "my A depended on x." A is a constant, so is not dependent on any variable.mike1967 said:Homework Statement
Find a particular solution Yp of the given equation. Primes denote deriviate with respect to x
(method of flexible guess)
Homework Equations
4y''+4y'+y=3xe^x
The Attempt at a Solution
when I used y=Ae^x as guess my A depended on x
Why don't you try yp = Aex + Bxex?mike1967 said:So y=Axe^x gave me 12A+9Ax=3x
12A=0
9Ax=3x
does not work,
Before I go on to trying y=Ax^2e^x am I doing this right?
mike1967 said:Yp=3/9xe^x-4/9e^x right?
This is something you should get in the habit of checking for yourself. You've already done all the hard work. If 4yp'' + 4y' + yp [itex]\equiv[/itex] 3xex, then your solution is correct.mike1967 said:Yp=3/9xe^x-4/9e^x right?
The Differential Equations Method of Flexible Guessing is a mathematical technique used to solve differential equations by making a "flexible" guess for the solution and then refining it through multiple iterations.
The method involves making an initial guess for the solution of the differential equation and then substituting it into the equation. The resulting equation is then solved for the unknown coefficients in the guess, which are adjusted to improve the accuracy of the solution. This process is repeated until a sufficiently accurate solution is obtained.
This method can be used to solve any type of ordinary differential equation, including linear, non-linear, first-order, and higher-order equations.
The Differential Equations Method of Flexible Guessing is a powerful technique for solving differential equations because it allows for a flexible and iterative approach, making it possible to obtain accurate solutions for a wide range of equations. It also does not require any special mathematical knowledge or advanced techniques, making it accessible to a wide range of users.
While the Differential Equations Method of Flexible Guessing is a useful tool, it does have some limitations. It may not work for extremely complex or non-linear equations, and the accuracy of the solution depends on the initial guess and the number of iterations performed. It is also not always possible to find an exact solution, and in some cases, an approximate solution may be obtained.