Welcome to our community

Be a part of something great, join today!

[SOLVED] Solving an IVP for a system of ODEs

krish

New member
Jun 26, 2013
6
Hello, I am having trouble solving the below IVP, particularly I am confused with the w:

du/dt = v - w(t-5)

dv/dt = 2 - u(t)

u(0)=0, v(0)=0

Any help would be great. Thank you.
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
What is \(\displaystyle w\) ? ,is it a constant or a function of $t$ ?
 

krish

New member
Jun 26, 2013
6

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667

krish

New member
Jun 26, 2013
6
Aha , try differentiating one of the equations and tell me if you got any ideas .
So I differentiated the second equation with respect to t:
v'' = -du/dt

Then I substitute first equation for du/dt:

v'' = -(v - w(t-5)) = -v + w(t-5)
v'' + v - w(t-5) = 0

Does it become: v'' + v = wt - 5w ? How does keeping the w matter?

And then I solve the IVP. Is this correct? But what if w is a function of t? Then I am confused, is that possible? Thank you for answering.
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
So I differentiated the second equation with respect to t:
v'' = -du/dt

Then I substitute first equation for du/dt:

v'' = -(v - w(t-5)) = -v + w(t-5)
v'' + v - w(t-5) = 0

Does it become: v'' + v = wt - 5w ? How does keeping the w matter?

And then I solve the IVP. Is this correct? But what if w is a function of t? Then I am confused, is that possible? Thank you for answering.
That seems a not-easy problem to deal with if we try the other differentiation we get

\(\displaystyle u''+ut = 2- w \)

The problem will get more complicated if assumed that $w$ a function because we have a three functions and two equations !

- - - Updated - - -

It might be solvable by Laplace but I don't know whether it is an acceptable solution ?
 

krish

New member
Jun 26, 2013
6
That seems a not-easy problem to deal with if we try the other differentiation we get

\(\displaystyle u''+ut = 2- w \)

The problem will get more complicated if assumed that $w$ a function because we have a three functions and two equations !

- - - Updated - - -

It might be solvable by Laplace but I don't know whether it is an acceptable solution ?
Can w(t-5) be the Heavyside unit function?
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
Can w(t-5) be the Heavyside unit function?
I don't know there is no indication , that depends on the source.
From Where did you get that problem ?
 
Last edited:

krish

New member
Jun 26, 2013
6
I don't know there is no indication , that depends on the source.
From Where did you get that problem ?
It's in the review questions in my Differential Equations textbook.
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
It's in the review questions in my Differential Equations textbook.
Ok , tell me the name of the textbook and the page number .
 

krish

New member
Jun 26, 2013
6
Ok , tell me the name of the textbook and the page number .
Differential Equations (From Engineering Viewpoint) - Dr. R.C. Shah
Page 309