5) Let F(t) te), te,t >for t e R. Find (t)dt. 0 te, tet, tdt 0
5. Let F(x) = Lt tet-2+tº +1 Edt, find F'(2) tt +3
Find the solution of 2ty' – 4y = 4t4eť, y(1) = 0. OA tet? tet – et OC tet– et? OD t² et² 2t2 OE eta — e
نه 2 5. Let F(x) = - [ « tet-2 + t3 +1 dt, find F'(2). tt + 3
g3ه 5. Let F(x) = وب tet-2 + t3 +1 - dt, find F (2). tt + 3
1. Find the Laplace transform of: f(t) = tet sin 2t u(t)
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE (1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1) 7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1)
any help on these two questions please?? 4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b) Find the general real solution of the linear ODE x(t)-Ax(t) + b(t). (c) Solve the initial value problem x(t) = A2(t) + b(t), x(0) = (-2,0,2)T 4.5: Determine the general solution of the ODE x"(t)-x"(t)-r(t) + x(t) = t cost. 4.4: Let 1 0 1 and b(t)- -1 1 0...
3. (25 Points) Find f(t). f(0) + f(t - 1)f(t)dt = t. Hint: The second term on the left side is a convolution and it might be helpful to use the Laplace Transform. 1 4. (10 Points) Solve the initial value problem by Laplace transform techniques. x" + 5x' + 4x = 0;x(0) = 1,x'(0) = 0. I 5. (15 Points) Find a series solution for the following differential equation. Calculate the radius of convergence. 2(x - 1)y' = 3y...