Examples of using General 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 you see that once you know the pattern, or once you know that this is going to be the general solution, they're pretty easy to solve.
The range has been designed to provide a general solution to the most commonly found daily needs.
So our particular solution, given these initial conditions, were, or are, or is y of x is equal to-- this was a general solution-- e to the minus 2x times-- we solved for c1.
Get your general solution.
But it's not the general solution.
So this is the general solution to this differential equation.
And so our general solution-- I will call that h.
Now let's take the derivative of our general solution.
When we have two real roots, then this is the general solution.
Now my question to you is, is this the most general solution?
And once you figure out the r's you have your general solution.
So that at least gives you an intuitive feel of why this isn't the general solution.
That the general solution of this non-homogeneous equation is actually the general solution of the homogeneous equation plus a particular solution. .
And then you get the general solution for this fairly intimidating-looking second order linear nonhomogeneous differential equation with constant coefficients.
It is our general solution C1e to the 4x plus C2e to the minus x plus our particular solution we found.
And then add them to the general solution for the homogeneous equation, if this was a 0 on the right-hand side.
Actually, let me erase some of this, just so that we can go from our general solution to our particular solution. .
So the general solution to this differential equation is y squared over 2 minus x squared over 2 is equal to c.
Maybe my general solution is just y is equal to some constant times e to the minus 2x, using my one solution. .
We know that the general solution to the homogeneous equation is C1e to the 4x plus C2e to the minus x, right?