Converting differential equations to matrix forms

[Brainwave22]

Please sir/ma, I really need the solution urgently. the ones I can solve are the single ones not coupled like this below.

Express the following system of coupled 2nd order scalar differential equations in matrix form.

u''+5u'+u-2v=0
v''+2v'-3u+v=0

 

[Brainwave22]

Please help me in solving this differential equation problem. I can solve the one in this form

X’’+3x’-4x=5sin2t.

It goes like this

Set x=x₁
x’₁ = x₂
x’₂ = x’’₁ = 5sin2t+4x₁-3x₂

Then the matrix form is as follows

=

Note that x’ implies first derivative of x.


Now this is the problem I need to solve which I don’t know how to go about it.

Express the following system of coupled 2^nd order scalar differential equations in matrix form.

u’’+5u’+u-2v=0
v’’+2v’-3u+v=0

Also note that v’ and u’ are the first derivatives of u and v.

 

[Deleted member 4993]

Please help me in solving this differential equation problem. I can solve the one in this form

X’’+3x’-4x=5sin2t.

It goes like this

Set x=x₁
x’₁ = x₂
x’₂ = x’’₁ = 5sin2t+4x₁-3x₂

Then the matrix form is as follows

=

Note that x’ implies first derivative of x.

Now this is the problem I need to solve which I don’t know how to go about it.

Express the following system of coupled 2^nd order scalar differential equations in matrix form.

u’’+5u’+u-2v=0
v’’+2v’-3u+v=0

Also note that v’ and u’ are the first derivatives of u and v.

Suppose

x₁ = u
x₂ = u'
x₃ = u"
x₄ = v
x₅ = v'
x₆ = v"

Now continue.....

 

[stapel]

Then the matrix form is as follows

=

Please note that we cannot access files on your hard drive. Sorry.

 

[Ishuda]

Please sir/ma, I really need the solution urgently. the ones I can solve are the single ones not coupled like this below.

Express the following system of coupled 2nd order scalar differential equations in matrix form.

u''+5u'+u-2v=0
v''+2v'-3u+v=0

You can solve as a single matrix equation as Subhotosh Khan hinted or you can solve it as a coupled equation. For the coupled equation, let's use your example
x’’+3x’-4x=5sin(2t)
which, following your work, let x1=x, x2=x',
\(\displaystyle \overset{\rightarrow}{x}=\begin{pmatrix}x_1\\ x_2 \end{pmatrix}\).
Then
x₁' = x₂
x₂' = x₁''= 5sin2t+4x1-3x2
or, in matrix form
\(\displaystyle \overset{\rightarrow}{x}'\)=\(\displaystyle \begin{pmatrix}0& 1\\ 4& -3 \end{pmatrix}\)\(\displaystyle \overset{\rightarrow}{x}+\begin{pmatrix}0\\ 5sin(2t)\end{pmatrix}\)
=\(\displaystyle \begin{pmatrix}0& 1\\ 4& -3 \end{pmatrix}\)\(\displaystyle \overset{\rightarrow}{x}+\begin{pmatrix}0& 0\\ 0& 5 \end{pmatrix}\begin{pmatrix}1\\ sin(2t)\end{pmatrix}\)

Can you continue from there?