please do Q3. AND Q4 B & C AS SOON AS YOU CAN
THANK YOU
differential equations Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral **F¢)} = [" e stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = Ost<4 t24 Complete the integral(s) that defines {f(t)}. {f(t)} = o Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)
please answer all 4 i really need it. its greatly appreciated Les ) be a function on 10,6). The Laplace transform of t is the function F defined by the integral F(0) - Sa-mat. Use this definition to determina the Laplace transform of the following function. -- The Laplace transform of F®-(Type an expression using s as the variable.) It is defined for >(Type an integer or a fraction.) Let (U) be a function on (0.00). The Laplace transform of...
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
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)
DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are proficient in DIFFERENTIAL EQUATIONS should even attempt to solve. No beginners or amateurs allowed. Please write clearly and legibly. No sloppy Handwriting. I must be able to clearly and easily read your solution and answer. Circle final answer. 7.2.10 Question Help Let fly be a function on [0, 00). The Laplace transform of fis the function F defined by the integral F(s)= c-stf(t)at. Use this definition to 0 determine the Laplace...
The following has 3 exercises and each exercise consists of multiple parts. please take into consideration all 3 exercises and answer each and every part of each exercise including the subquestions found in it!! Exercise 1 Find the Laplace transform of the following functions: 1. f(t) = 5t3e-46 2. f(t) = cos(26)U(t - T) 3. k(t) = {2-1, t<2 t> 2 4. f(t) = etsin (3) Exercise 2 Use Laplace transforms to compute the solution y(t) of the initial value...
· Evaluate the following inverse Laplace transform 2-1 S 5s + 3 ) 1 s2 + 4s +5% ] Solve the following system of differential equations S x' – 4x + y" | x' + x + y = 0, = 0. Use the method of Laplace Transforms to solve the following IVP y" + y = f(t), y(0) = 1, y'(0) = 1, where f(t) is given by J21 0, t>1. f(t) = {t, Ost<1, PIC.COLLAGE
this is from differential equations. if someone can do the whole sheet except for question 10 if you could do two to of them, I would greatly appreciate it. thank you in advance. 5. Solve the equation 7" +2+y = 2+32) (do tiot use the Laplace transform.) 6. Use the definition of Laplace transform to find LFO), where f(t) =t if 0 <t<1, () = 1 if IcI<3 and fit -2 ift 3. -1) dx + 3yle" + 1)dy =...
Question: Equations: My attempt (sorry for uneatness) : Tutorial questions - Sine and Cosine transforms 9. U se the Fourier Inversion Theorem to prove for a real-valued odd function f(t) that F.(w) sin wt du at points of continuity. (Hint: first simplify the integral expression for F(w).) Fourier Inversion Theorem. At points where f0) is continuous, is that t at t=( iwt extra te Fo F(w)-マ27: J-0,f(t)e-iwt dt = F(f(t)) w) is called the Fourier cosine transform of f(t). Similarly,...
PLEASE MAKE SURE TO ANSWER ALL EMPTY BOXES SHOWN ON THE PROBLEM PLEASE AND THANK YOU (1 point) Use the Laplace transform to solve the following initial value problem: y" – 2y + 10y = 0 y(O) = 0, y' (O) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = By completing the...