Question

state whether the following equation is quadratic equation in X?.2x*2 + 5/2x-√3=0​

Answer 1

Answer:

Find Laplace transform of L[3+t]We write cos(4t) = f(t), say. Now if L(f(t)) = F(s), then, by theorem on derivatives of Laplace transforms, we have L(t.f(t)) = -F'(s), where the ' denotes derivative with respect to s. We know that

L(cos(4t)) = s/(s^2+16). Therefore in view of the above theorem, we get that

(s^2–16)/(s^2 +16)^2. Similarly applying the theorem twice more we get L(t^3.cos(4t)).