Differential Equations Question

[paintballvet18]

Solve for x(t) and y(t).

 

[Deleted member 4993]

View attachment 17873

Solve for x(t) and y(t).

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment

 

[paintballvet18]

Sure...

So the easy thing to do is solve for y'(t) in the top equation:

x'(t) =- pi - y(t) + 5.696592654
x'(t) + y(t) =- pi + 5.696592654
y(t) =- pi + 5.696592654 - x'(t)
differentiate

y'(t) = -x"(t)

plug into bottom formula

-x"(t) = - (x(t) - 6.173)^2 - (- pi + 5.696592654 - x'(t)) + 2.805

Now I don't know what to do.

 

[topsquark]

Can you rewrite this in the form ax'' + bx ' + cx = d?

-Dan

 

[paintballvet18]

Can you rewrite this in the form ax'' + bx ' + cx = d?

-Dan

-x"(t)-x'(t)+x(t)²-12.346x(t) = pi - 40.997521654

-x"-x'+x²-12.346x = pi - 40.997521654

 

[HallsofIvy]

Can you rewrite this in the form ax'' + bx ' + cx = d?

-Dan

No, because it is a non-linear equation!

 

[Deleted member 4993]

No, because it is a non-linear equation!

I missed that important point too! Don't tell Jomo please.

 

[HallsofIvy]

paintballvet18, there are no general methods for solving non-linear equations. Typically you use approximation methods.

 

[topsquark]

No, because it is a non-linear equation!

That little ^2 always gets me.

Thanks for the catch!

-Dan

 

[Deleted member 4993]

Let's all keep quite and Jomo wouldn't know.....