1 Use the Laplace Transform to solve the following system of DEdx/dt=x+4*y , dy/dt=4*x+y, x(0)=-1...

Question

1 Use the Laplace Transform to solve the following system of DE
dx/dt=x+4*y , dy/dt=4*x+y, x(0)=-1 ,y(0)=0
2. Same as in (1) for
dx/dt=x-3*y, dy/dt=-3*x+y , x(0)=-1, y(0)=-1
3. Solve y''+2*y'+2*y=delta(t) ,y(0)=0, y'(0)=0
(OPTIONAL: y(0)=0, y'(0)=1)
4. Solve numerically
y'= 2*x+x*y+y^2 , y(0)=1 on [0,1] with step size h=1/3.

(Plz refer to the lecture notes, solve problems step by step using the same way as stated in the lecture notes)

005_a5qxazo-gmyuwljv.pdf 005_dz2xazo-gb0wnslt.pdf

David · Accepted Answer

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1   
4
4
0 1
0 0
Apply the Laplace transformation to the first part,
4
4
 0 4
1 1 4
1 1
4
Apply the Laplace transformation to the second part,
dx
x y
dt
dy
x y
dt
x
y
L L x y
L L x L y
s L x x L x L y
s L x L y
s L x
L y
x
x


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4
 0 4
L L x y
s L y y L x L y
y
 
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 
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2
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1  4
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s L y L x
s L x
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s L x s L x
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     
2
2
1 16 1
1 16 1
s L x L x s
s L x s
    
     
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2
2
2
2
1
1 16
cosh 4
4 1
And plugging   in 1  4
1
4 1
1  4
1
1 16 4
1 16 4
4
1 16
sinh 4
sinh 4
Therefore,

1 Use the Laplace Transform to solve the following system of DE dx/dt=x+4y , dy/dt=4x+y, x(0)=-1 ,y(0)=0 2. Same as in (1) for dx/dt=x-3y, dy/dt=-3x+y , x(0)=-1, y(0)=-1 3. Solve...

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1 Use the Laplace Transform to solve the following system of DE dx/dt=x+4*y , dy/dt=4*x+y, x(0)=-1 ,y(0)=0 2. Same as in (1) for dx/dt=x-3*y, dy/dt=-3*x+y , x(0)=-1, y(0)=-1 3. Solve...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment

1 Use the Laplace Transform to solve the following system of DE dx/dt=x+4y , dy/dt=4x+y, x(0)=-1 ,y(0)=0 2. Same as in (1) for dx/dt=x-3y, dy/dt=-3x+y , x(0)=-1, y(0)=-1 3. Solve...