D’Alembert’s reduction principle

[mathrocks]

Hey guys, I'm stuck on this problem! I have no idea how to even go about solving it. I tried searching the net for D'Alembert's principle but nothing was helpful. Any suggestions on how to go about solving it will be much appreciated!

Find with the aid of D’Alembert’s reduction principle the FS of the ODE system.

x₁(t)= x₁(t)/t - x₂(t)

x₂(t)= x₁(t)/t²+ 2x₂(t)/2

for which a particular solution x(t)=(t², -t) is known.

 

[elibj123]

Is this an ODE System or algebric equations System?

What is FS (sorry I don't know :P)?

 

[mathrocks]

Is this an ODE System or algebric equations System?

What is FS (sorry I don't know :P)?

this is an ODE. FS stands for fundamental system.

 

[Arturgower]

There are no derivatives, therefore this is not a ODE. Secondly (t^2,-t) is not a solution.
Missing derivatives, and the second line should be,
x_2' = x_2/t^2 + 2 x_2/t

 

[elibj123]

that's the point,
(t^2,-t) is the solution of the algebric equations (as he written them)
so I'm a bit confused

 

[HallsofIvy]

Mathrocks, do you mean
dx₁(t)/dt= x₁(t)/t - x₂(t)

dx₂(t)/dt= x₁(t)/t²+ 2x₂(t)/2