We are given the initial value y(0) = 2. Substituting this value and solving for L{y}...
Consider the initial value problem Let L[y(t)] = Y(3), then Y(s) equals Select one: 2s +2 a. O b. 3s +1 s(232 + s +3) 2s2 + s +1 OC s(2s2 + 8 +3) O d. 2s +1-2/3 252 +8 e. 28 +1 -4/5 28² +8
Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem: 1, y' + 9 = 0<t<T 0,7 <t< y(0) = 5, y'(0) = 4
Tutorial Exercise Use the Laplace transform to solve the given initial-value problem. y' + 5y = et (0) = 2 Step 1 To use the Laplace transform to solve the given initial value problem, we first take the transform of each member of the differential equation + 6y et The strategy is that the new equation can be solved for ty) algebraically. Once solved, transforming back to an equation for gives the solution we need to the original differential equation....
Given the initial value problem below, what is L{f}or Y? Write L{f}or Y. y - y - 2y = 0; y(0) = - = 5 LaTeX : +7+28 (8-2)(s+1) None of the above LTY. -7+25 LaTeX: ' (3-2)(3-1) 7-28 Lalen. (8-2)(8 - 1) LaTeX: 7-28 (8+2)(8-1)
We can now rewrite L{y} as follows. (1) + (-) L{y} = S-5 S + 4 Next, to solve for y, we apply the inverse Laplace transform L-1 to each term. (1) y(t) = -1, + 4-1) + We now recall the following, where a and b are constants. 1 • By Theorem 7.2.1.: = eat • By linearity of L-1, L-1{bs} = 6L-1{s} Applying these gives the following result. y(t) =
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we haven We obtain the equation + given by Solving the resulting first order linear equation for u we obtain the general solution with arbitrary constant Then transforming back into the variables 2 and y and using the initial condition to find C Finally we obtain the explicit solution of the initial value problem as
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) = 2, 7(0) = -4. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, Y" – 8y' + 25 y=0, y(0) = 5, y(0) 3. a. (4/10) Find the Laplace Transform of the solution. Y(s)...
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
Differential Equations Transform the given initial value problem into an algebraic equation for Y = L{y} in the s-domain. (a) /'"-6y" +1ly - 6y=et, y(0) = '0) = Y(0) = 0 (b) y" + 1" + y + y = 0, y(0) = 1, y(0) = 0, y"0) = -2
You found the solution to the initial value problem to be -2s S 1 [e y(t) = L-1 94 +10 Evaluate y(1). O y(1) = 1 Oy(1) = -1 O y(1) = 0 y(1) = -2 Oy(1) = 2