Examples of using Particular solution in English and their translations into Hebrew
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And now we have our particular solution.
The particular solution was minus 5/17 sine of x plus 3/17 cosine of x.
And then we have our particular solution.
This particular solution, when you put it in the left-hand side, will equal this term.
This was another particular solution we found.
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.
So we know the particular solution when 0's on the right-hand side.
So what's a good guess for a particular solution?
And that would be the particular solution, then, for this differential equation.
Here we can view this as a particular solution.
Let's see if this particular solution satisfies the second initial condition.
So we're just defining j of x to be a particular solution.
And if someone wanted a particular solution, they would have to give you two initial conditions.
Basic notions: equations of the first order, general solution, initial value problem, particular solution.
You take a guess of a particular solution and then you solve for the undetermined coefficients.
So how do we get, in that last example,a j of x that will give us a particular solution, so on the right-hand side we get this.
And finally, this particular solution, when you put it on the left-hand side, will equal the 4x squared.
So if this is the general solution to the homogeneous equation, this a particular solution to the nonhomogeneous equation.
And we saw that that particular solution there, y particular, was minus 1/2 e to the 2x.
If there is no satisfaction and if there is no norm,it is up to each person to invent a particular solution, one that builds on his symptom.
We figured out that the particular solution in this case was minus x squared plus 3/2 x minus 13/8.
That the general solution of this non-homogeneous equation isactually the general solution of the homogeneous equation plus a particular solution.
Our solution is going to be equal to the particular solution, which is Ax squared, so that's minus 1x squared.
Our particular solution here could be that-- and particular solution I'm usinga little different than the particular solution when we had initial conditions.
So now we will actually be 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 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 generalsolution of a nonhomogeneous equation, to get the solution. .
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