Put the equation given in the form
The center will be (-f, -g)
If you would like to calculate 6/(x+1)-5/2=6/(3x+3), you can do this using the following steps:
6/(x+1)-5/2=6/(3x+3)
6/(x+1)-5/2=6/(3(x+1)) /*(x+1)
6 - 5/2 * (x+1) = 6/3
6 - 2 = 5/2 * (x+1)
4 = 5/2 * (x+1) /*2/5
4 * 2/5 = x + 1
8/5 - 1 = x
x = 8/5 - 5/5 = 3/5
The correct result would be 3/5.
First: the homogeneous solutions: the characteristic equation is4r^2 - 4r - 3 = 0which has roots r = 3/2, -1/2 hence the homogeneous solution isy = c1.exp(-x/2) + c2.exp(3x/2)
next you need the general form for the guess for yp and that isyp = A1cos(2x) + A2sin(2x)
Now substitute that into the equation and solve for A1, A2.
I have attached the graph. Your axis is x=-4 and the vertex is (-4,-30)
Hope that helps
