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3. Find the Laplace transform off, where f(t) = 3 + 2 if Ost <3, f(t) = 0 if 3 st < 6 and f is periodic with period 6. 4. Solve y" - 16y = 40e4t y(0) = 5, y(0) = 9 using the Laplace transform.
Find L(f) if f (t) equals ta sin (2t). Enclose arguments of functions, numerators, and denominators in parentheses. For example, sin (2 * x) or (a - b)/(1+n). Use an asterisk, *, to indicate multiplication. For example, 2* f (x), a* * (x+b) * (c*x+d), b* tan (a * ) or ea*r) * b. L (f) (s) QC
Find the Laplace transform of the given function. Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n). f(t) = S1, 0<t<8 t> 8 0,
differential equations Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 00 L{f(t)} = -192 e-stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = {6, ost<4 t24 Complete the integral(s) that defines L{f(t)}. L{f(t)} = Datet (" dt Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)
Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. y" + 16y S 1, 0 <t<T , YO) = 5, y' (0) = 9 0, <t<oo Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y (8) = Qe
Let f(t) be a function on [O...). The Laplace transform of f is the function F defined by the integral F(s) = e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. e3 Ost<2 f(t) = 4, 2<t for all positive si and F(s) = 2+ The Laplace transform of f(t) is F(s) = (Type exact answers.) 2+ c - 6 otherwise.
Chapter 6, Section 6.2, Question 17 Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem y" + 16 = 1,0<t< 10, <t < 0 y(0) = 3, y' (0) = 3 Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y($) = Qe
Chapter 6, Section 6.2, Question 18 Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. y" + 4y t, 0<t<1 y (0) = 9, y' (0) = 3 1,1<t<oo Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y() Q
Let f(t) be a function on [0, 0). The Laplace transform of f is the function F defined by the integral F(s) = e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. 0 est 0<t<1 f(t) = 1 <t for all positive sand F(s) = 1 + 5 -5 otherwise. The Laplace transform of f(t) is F(s) = (Type exact answers.)
Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. St, 0<t<1 y" + 4y = {i;isica , y0 = 8, Y' (0) = 6 Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y (3) = QE