For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = log2 (x)
Solve the given system of differential equations by systematic
elimination.
(D2 − 1)x
−
y
=
0
(D − 1)x
+
Dy
=
0
I had this as my answer and webassign rejected it:
(x(t), y(t)) = c_1e^t+e^{-\left(\frac{t}{2}\right)}\left(c_2\cos
\left(\frac{\sqrt{3}}{2}t\right)+c_3\sin
\left(\frac{\sqrt{3}}{2}t\right)\right),e^{-\left(\frac{t}{2}\right)}\left(\left(-\frac{3}{2}c_2-\frac{3\sqrt{3}.}{4}c_3\right)\cos
\left(\frac{\sqrt{3}}{2}t\right)+\left(\frac{-3}{2}c_3+\frac{3\sqrt{3}}{4}c_2\right)\sin
\left(\frac{\sqrt{3}}{2}t\right)\right)
Use the Laplace transform to solve the given system of
differential equations.
d2x/dt2 + x − y = 0
d2y/dt2 + y − x = 0
x(0) = 0, x'(0) = −4
y(0) = 0, y'(0) = 1