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Answer all questions (100 marks) 1. Given x(0) = 0 and transform. = 0, solve the...
Answer all questions (100 marks) 1. Given x(0) = 0 and transform. = 0, solve the following differential equation using Laplace d?x(t) dx +6 dt2 + 8x(t) = 2e-31 dt (20 marks) 2. Find the vo(t) in the network in Figure I using Laplace approach. 12 S 2 w O 1,(s) Ls) V.(5) Figure 1 (30 mrks)
Solve the PDE using laplace: (dw/dx)+(x*(dw/x)) =xu(t-1) w(x,0)=0 if x>=0 and w(0,t)=0 if t<=0
Solve the PDE using laplace: (dw/dx)+(x*(dw/x)) =xu(t-1) w(x,0)=0 if x>=0 and w(0,t)=0 if t<=0
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) f...
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i, where f(t)-〈0 otherwise. (b) z', +x-f(t), x(0) 0, z'(0)=1, where t/2 if 0 t< 6, 3 ift26 f(t)
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i,...
solve using laplace transforms x" +0.4x' + 2x = 1 - Hz(t) x(0) =0, x'0) =...
solve using laplace
transforms
x" +0.4x' + 2x = 1 - Hz(t) x(0) =0, x'0) = 0
2. Consider the pde 0 <а < о, w(z,0) — 0, w(0, t) - t> 0, xwf = 0, = t Wr = (a) Use separation of variables to...
2. Consider the pde 0 <а < о, w(z,0) — 0, w(0, t) - t> 0, xwf = 0, = t Wr = (a) Use separation of variables to show that w(x, t) exp(k(t where k is a constant. (b) Show that the above solution does not satisfy both the initial and boundary conditions. (c) Use Laplace Transforms to solve the above pde.
2. Consider the pde 0
y(t) is INCORRECT but x(t) is CORRECT DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are...
y(t) is
INCORRECT
but
x(t) is CORRECT
DIFFERENTIAL EQUATIONS / Linear Algebra
Only people that are proficient in DIFFERENTIAL EQUATIONS should
even attempt to solve. No beginners or amateurs allowed.
Please write clearly and legibly. No sloppy Handwriting. I must
be able to clearly and easily read your solution and answer.
Circle final answer.
BELOW is an example of what the answer should look very similar
to. should be in the same form basically.
example
7.10.4 Question Help Use the...
(b). Use the chain rule to find aw and as y = 8 cost, z =...
(b). Use the chain rule to find aw and as y = 8 cost, z = s sint when s= 1 and t=0 aw at where w = = 22 + y2 + z2, x = st,
use laplace transforms to solve ivp x" + 2x' - 15x = 6delta(t -9), x(0) =...
use laplace transforms to solve ivp x" + 2x' - 15x = 6delta(t -9), x(0) = -5, x'(0) = 7
Solve the initial value problem below using the method of Laplace transforms. w" - 2w' +...
Solve the initial value problem below using the method of Laplace transforms. w" - 2w' + w=5t +6, W( - 2) = 4, w'(-2) = 8 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. w(t) = (Type an exact answer in terms of e.)
Solve the initial value problem, x''+8x' +16x = 1 + 8(t-7), x(0) = x'(0) = 0....
Solve the initial value problem, x''+8x' +16x = 1 + 8(t-7), x(0) = x'(0) = 0. Click the icon to view the table of Laplace transforms. Write the solution to the initial value problem. Select the correct choice below and fill-in the answer boxes to complete your choice. (Type exact answers. Simplify your answers.) ift< ift< OB. X(t) = O A. X(t) = if <t< if t2 if t OD. X(t) = OC. X(t) = if t = if t...
Answer all questions (100 marks) 1. Given x(0) = 0 and transform. = 0, solve the following differential equation using Laplace d?x(t) dx +6 dt2 + 8x(t) = 2e-31 dt (20 marks) 2. Find the vo(t) in the network in Figure I using Laplace approach. 12 S 2 w O 1,(s) Ls) V.(5) Figure 1 (30 mrks)
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i, where f(t)-〈0 otherwise. (b) z', +x-f(t), x(0) 0, z'(0)=1, where t/2 if 0 t< 6, 3 ift26 f(t)
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i,...
solve using laplace
transforms
x" +0.4x' + 2x = 1 - Hz(t) x(0) =0, x'0) = 0
2. Consider the pde 0 <а < о, w(z,0) — 0, w(0, t) - t> 0, xwf = 0, = t Wr = (a) Use separation of variables to show that w(x, t) exp(k(t where k is a constant. (b) Show that the above solution does not satisfy both the initial and boundary conditions. (c) Use Laplace Transforms to solve the above pde.
2. Consider the pde 0
y(t) is
INCORRECT
but
x(t) is CORRECT
DIFFERENTIAL EQUATIONS / Linear Algebra
Only people that are proficient in DIFFERENTIAL EQUATIONS should
even attempt to solve. No beginners or amateurs allowed.
Please write clearly and legibly. No sloppy Handwriting. I must
be able to clearly and easily read your solution and answer.
Circle final answer.
BELOW is an example of what the answer should look very similar
to. should be in the same form basically.
example
7.10.4 Question Help Use the...
(b). Use the chain rule to find aw and as y = 8 cost, z = s sint when s= 1 and t=0 aw at where w = = 22 + y2 + z2, x = st,
Solve the initial value problem below using the method of Laplace transforms. w" - 2w' + w=5t +6, W( - 2) = 4, w'(-2) = 8 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. w(t) = (Type an exact answer in terms of e.)
Solve the initial value problem, x''+8x' +16x = 1 + 8(t-7), x(0) = x'(0) = 0. Click the icon to view the table of Laplace transforms. Write the solution to the initial value problem. Select the correct choice below and fill-in the answer boxes to complete your choice. (Type exact answers. Simplify your answers.) ift< ift< OB. X(t) = O A. X(t) = if <t< if t2 if t OD. X(t) = OC. X(t) = if t = if t...
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