Find the general solution of y" – 54"' + 6y' = 0. 8.8 A BRIEF TABLE...
Find the general solution of y(4) + 24" +y= 0. 8.8 A BRIEF TABLE OF LAPLACE TRANSFORMS (0) F(8) - (s > 0) " ni! (x > 0) (n = integer > 0) 1", p > 1 T(+1) (x > 0) 604 11! (s > 0) (n integer > 0) CON WI N ya wa (x > 0) sint (x > 0) Al cost NA (6 A)? + w (8 > A) sinut (> ) cosh bt (8 > 161)...
Find 2-1 s +5 82 + 6s + 18 8.8 A BRIEF TABLE OF LAPLACE TRANSFORMS F(s) (s > 0) + (s > 0) (11 integer > 0) 1'(p+1) (P+1) (s >0) 1 094 (s >a) 8a n! (s = a)"+1 (* > 0) an integer >> 0) CONWt (3 > 0) sint (8 > 0) put coswt (8 - 1)? twa (* > 1) en sint (s > ) (8 - x)? Twº cosh (s > 100 sinh bt...
please use the table to solve the question Problem 5. Find the inverse transform of the function F(s) = - $+1 352 + 12 TABLE OF LAPLACE TRANSFORMS f(t) F(S) (s > 0) -in EE (s > 0) (n = integer > 0) IP, p>-1 r(p+1) s(p+1) (s > 0) - ear (s > a) V S-a 1241 (s > 0) (s -a)+1 (n = integer > 0) coswt (s > 0) V s² + w? 3 sinat (s >...
Find the Laplace transform of the function f(t). f(t) = sint if 0 St< $41; f(t) = 0 ift> 41 Click the icon to view a short table of Laplace transforms. F(s)=
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...
Q4 a) Find the general solution of the differential equation Y') + {y(t) = 8(6+1)5; 8>0. Y'8 8 >0. 8(8-1)3 b) Find the inverse Laplace transform y(t) = £ '{Y(3)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te, y(0) = 0, y(0) = 1, for t > 0. You may use the above results if you find them helpful....
1. problem 2. and 3. as follows Find the inverse Laplace transforms of the following function: 2w7 F(s) = s($2 + 2Cwns + wa) "US 25 (0<5<1) Solve the following differential equation: * + 2wni+wn?x=0, (0) = a, (0) = b where a and b are constants, and 0 << < 1. Solve the following differential equation: ö + 3 + 40 = 2 sint, x(0) = 0, 0) = 0
Find the Laplace transform of the function f(t). f(t) = sint if o St<$21; f(t) = 0 if t> 21 Click the icon to view a short table of Laplace transforms. F(S) =
Express the following functions in terms of unit step functions and find the Laplace transforms. 2 f(t)= 0 0<ts 1<t<21 t> 21 sint (12 marks)
Solve the given initial value problem using the method of Laplace transforms. y'' + 3y' +2y = tu(t-3); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem. y(t) = | Properties of Laplace Transforms L{f+g} = £{f} + L{g} L{cf} = CL{f} for any constant £{e atf(t)} (s) = L{f}(s-a) L{f'}(s) = sL{f}(s) – f(0) L{f''}(s) =...