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2 answers:
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Answer:
Solution given.
centre (h,k):(2,-1)
another point is (6,-1)
radius (r)==4
we have
equation of a circle is:
(x-h)²+(y-k)²=r²
(x-2)²+(y+1)²=4²
(x-2)²+(y+1)²=16is a required equation of a circle.
Answer:
Step-by-step explanation:
We will use the reduction of order to solve this equation. At first, we need a solution of the homogeneus solution.
Consider the equation We will assume that the solution is of the form
. If we plug this in the equation, we get
Since the exponential function is a positive function, and A should be different to zero to have non trivial solutions, we get
By using the quadratic formula, we get the solutions
So one solution of the homogeneus equation is of the form . To use the reduction of order assume that
where . We calculate the derivatives and plug it in the equation
If we rearrange the equation we get
Since is a solution of the homogeneus equation we get
If we take w = v', then w' = v''. So, in this case the equation becomes
Note that so
. Since
cannot be zero, this implies
w' =0. Then, w = K (a constant). Then v' = K. So v=Kx+D where D is a constant.
So, we get that the general solution is
where C, F are constants.