Examples of using Particular solution in English and their translations into Thai
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Colloquial
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Ecclesiastic
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Ecclesiastic
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Computer
But the important realization is that you just have to find the particular solutions for each of these terms and then sum them up.
First of all, the particular solution to this nonhomogeneous equation, we could just take the sum of the three particular solutions.
So what's a good guess for a particular solution?
Let's see if this particular solution satisfies the second initial condition.
And that would be the particular solution, then, for this differential equation.
So we know the particular solution when 0's on the right-hand side.
So if this is the general solution to the homogeneous equation, this a particular solution to the nonhomogeneous equation.
That the general solution of this non-homogeneous equation is actually the general solution of the homogeneous equation plus a particular solution.
and you end up with your particular solution.
You can kind of say conditions or points where we know that the particular solution to this differential equation are satisfied.
We have our particular solution to this-- sorry where did I write it-- to this differential equation with these initial conditions.
Our solution is going to be equal to the particular solution, which is Ax squared, so that's minus 1x squared.
So if I wanted a particular solution, how can I solve for two variables if I'm only given one initial condition?
So since we have a polynomial here that makes this differential equation nonhomogeneous, let's guess that a particular solution is a polynomial.
And we found that the particular solution in this case-- and this was a fairly hairy problem-- was minus 5/17 x plus 3/17.
So using these conditions, a point where this function crosses through, we can now give you the particular solution to this differential equation.
So you can say that x minus-- so our any solution x minus the particular solution of x is a member of our null space.
So now we will actually be able to figure out a particular solution, or the particular solution, for this differential equation.
And if you want the particular solution, people normally give you initial conditions or they give you points on the function and then you can substitute back.
So if you just had this first initial condition, say fine, my particular solution is y is equal to A times e to the minus 2x.