Question

Show all your work to receive full credit. 1-2. Find the inverse Laplace transform of the given function. 1. $F(s) = \frac{6s^2 + s + 12}{s(s-1)(s^2 + 4s + 6)}$ 2. $F(s) = \frac{3 - 4s + s^2}{(s-2)^3}$ 3-4. Use the Laplace transform to solve the initial-value problem. 3. $y'' - 4y' + 4y = te^{2t}$; $y(0) = 2$, $y'(0) = 1$ 4. $y'' + 6y' + 5y = 12e^t$; $y(0) = -1$, $y'(0) = 7$

          Show all your work to receive full credit.
1-2. Find the inverse Laplace transform of the given function.
1. $F(s) = \frac{6s^2 + s + 12}{s(s-1)(s^2 + 4s + 6)}$
2. $F(s) = \frac{3 - 4s + s^2}{(s-2)^3}$
3-4. Use the Laplace transform to solve the initial-value problem.
3. $y'' - 4y' + 4y = te^{2t}$; $y(0) = 2$, $y'(0) = 1$
4. $y'' + 6y' + 5y = 12e^t$; $y(0) = -1$, $y'(0) = 7$

Show all your work to receive full credit.
1-2. Find the inverse Laplace transform of the given function.
1. F(s) = (6s^2 + s + 12)/(s(s-1)(s^2 + 4s + 6))
2. F(s) = (3 - 4s + s^2)/((s-2)^3)
3-4. Use the Laplace transform to solve the initial-value problem.
3. y” - 4y' + 4y = te^2t; y(0) = 2, y'(0) = 1
4. y” + 6y' + 5y = 12e^t; y(0) = -1, y'(0) = 7

Added by Lisa S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/10/2022

Step 1

Let's rewrite F(s) as: F(s) = A/s + B/(s - 1) + (Cs + D)/(s^2 + 4s + 6) Now, we need to find the constants A, B, C, and D. To do this, we clear the denominators: 6s^2 + s + 12 = A(s - 1)(s^2 + 4s + 6) + Bs(s^2 + 4s + 6) + (Cs + D)s(s - 1) Now, we can solve for Show more…

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Show all your work to receive full credit. 1-2. Find the inverse Laplace transform of the given function. F(s)=(6s^(2)+s+12)/(s(s-1)(s^(2)+4s+6)) F(s)=(3-4s+s^(2))/((s-2)^(3)) 3-4. Use the Laplace transform to solve the initial-value problem. y^('')-4y^(')+4y=t^(5)e^(2t);,y(0)=2,y^(')(0)=1 y^('')+6y^(')+5y=12e^(t);y(0)=-1,y^(')(0)=7 Show all your work to receive full credit. 1-2. Find the inverse Laplace transform of the given function 6s2+5+12 1.Fs)= 5(5-1)(s2+4s+6) 2.F(s)=3-45+s2 (s 2)3 3-4. Use the Laplace transform to solve the initial-value problem. 3.y"-4y+4y=te; y0=2,y0=1 4.y"+6y+5y=12e;y0)=-1,y0=7