Register to reply

Examples of system of linear differential equations with periodic coefficients

Share this thread:
Jul16-11, 01:13 AM
P: 14
hi ,
can anybody give me some examples of 'systems of linear differential equations with periodic coefficients'? i dont know how to solve it.. where can i get problems and solutions on this?
Phys.Org News Partner Science news on
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
Jul16-11, 07:22 AM
Sci Advisor
PF Gold
P: 39,361
You mean something like
[tex]sin(t)\frac{dx}{dt}+ (1- t^2)\frac{dy}{dt}= e^t[/tex]
[tex]cos(t)\frac{dx}{dt}+ t\frac{dy}{dt}= t[/tex]?

You will want to try to reduce this to a single equation in either x only or y only.
Essentially, use "Gaussian reduction" just as you would for an algebraic system.

Or you could try writing the system as a matrix equation:
[tex]\begin{bmatrix}sin(t) & 1- t^2 \\ cos(t) & t\end{bmatrix}\begin{bmatrix}\frac{dx}{dt} \\ \frac{dy}{dt}\end{bmatrix}= \begin{bmatrix}e^t \\ t\end{bmatrix}[/tex]
and use the same matrix methods you would for the "constant coefficient" case. Of course, you would have to remember that, since the coefficient matrix now depends on t, d(AX)/dt= X(dA/dt)+ A(dX/dt), not just "A(dX/dt)".

Register to reply

Related Discussions
Definition of variable coefficients in linear differential equations Differential Equations 4
System of Linear Differential equations Calculus & Beyond Homework 5
Systems of Linear Homogenous Differential equations with Constant Coefficients Differential Equations 1
Differential equations. linear system. Calculus & Beyond Homework 1
System of linear equations with complex coefficients Precalculus Mathematics Homework 3