Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the...
Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the differential equation. Recall: h(t - a) is the unit step function shifted to the right a units. y" + 25y = (4t – 8)h(t – 2) - (4t – 12)h(t – 3), y(0) = y' (O) = 0 Y(S) =
Apply the Laplace transform to the differential equation, and solve for Y(s) y'25y 2(t 4)u4(t) 2t 8)us(t), y(0) = y'(0) = 0 Y(s) = Preview syntax error Apply the Laplace transform to the differential equation, and solve for Y(s) y'25y 2(t 4)u4(t) 2t 8)us(t), y(0) = y'(0) = 0 Y(s) = Preview syntax error
where h is the Use the Laplace transform to solve the following initial value problem: y"+y + 2y = h(t – 5), y(0) = 2, y(0) = -1, Heaviside function. In the following parts, use h(t – c) for the shifted Heaviside function he(t) when necessary. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. L{y(t)}(s) = b. Express the solution y(t) as the...
1. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): 1/(t) + 14y(t) = sin(34) + cos(5t). 2. Use the Laplace transform to convert the following differential equation into 8-space and then solve for Y(): y") + 3y(t) = (2)
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1
1. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): vy(t) +14y(t) = sin(3) + cos(54) (1) 2. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): "(t) + 3y(t) = 2)
6) a) Solve the following differential equation using the Laplace transform method. dy = 1.87ylt) + 4.05 y0) = 1 You may need the expression, 1.05 4.05 s(s - 1.87) 1.87(s - 1.87) 4.05 1.87s [8 marks] b) Solve the following differential equation using the Laplace transform method. dºy + 2.61X + 6.55y(t) = 0 y(0) = 1, y'(0) = 1 2. You may need the expression, s +1 +2.61 52 +2.615 +6.55 *2.01.2015 - | 1+2,61 (8+2.01) + ((6.55-...
both O Apply Laplace transform on sides of the following differential equation: - eo (t) + R₂. C. deo(t) = R. e(t) dt G(s) in order transfer to find function. & (6) Eics)
Given the differential equation y' + 367 - ezt, y(0) = 0, y'(0) = 0 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-1{Y(s)} g(t) =
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2