Examples of using Particular solution in English and their translations into Arabic
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Colloquial
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Political
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Ecclesiastic
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Ecclesiastic
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Computer
So this is the particular solution.
The particular solution was minus 5/17 sine of x plus 3/17 cosine of x.
This was another particular solution we found.
And let's see whathappens when we take A times x minus some particular solution to this.
It's a particular solution to the equation.
So how do you figure out that particular solution?
Let's say j is a particular solution to this differential equation.
And now I can substitute in here, and let's see if I can solve for A,and then I will have my particular solution.
There's only one particular solution right there.
So since we have a polynomial here that makes this differential equation nonhomogeneous,let's guess that a particular solution is a polynomial.
We're saying that this is a particular solution to this equation.
But this particular solution comes with costs that we haven't yet well quantified.
So if I haven't, then our particular solution, we now know.
We said j is a particular solution for the non-homogeneous equation, or that this expression is equal to g of x.
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.
And of course, any particular solution to this when you multiply it by A is also going to be equal to b.
So if this is the general solution to the homogeneous equation, this a particular solution to the nonhomogeneous equation.
So we know the particular solution when 0's on the right-hand side.
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.
And finally, this particular solution, when you put it on the left-hand side, will equal the 4x squared.
But what's interesting is this particular solution has no i's anywhere in it.
Our particular solution here could be that-- and particular solution I'm using a little different than the particular solution when we had initial conditions.
So now we will actuallybe able to figure out a particular solution, or the particular solution, for this differential equation.
So if I wanted a particular solution, how can I solve for two variables if I'm only given one initial condition?
And that would be the particular solution, then, for this differential equation.
First of all, the particular solution to this nonhomogeneous equation, we could just take the sum of the three particular solutions. .
Let's see if this particular solution satisfies the second initial condition.
We figured out that the particular solution in this case was minus x squared plus 3/2 x minus 13/8.
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 we're going to focus just now on the particular solution, then we can later add that to the general solution of a nonhomogeneous equation, to get the solution. .