Differential Equation: System of Equations

For this problem state the method you used and show the work required to obtain the answer. Find the general solution for this system: this is a matrix x'= 3y+z y'= x+z+2y z"= 3y+x

Getting started with ODE

I would like someone to introduce me to ODE and answer questions as they arise.

Initial Value Problem, Ordinary Differential Equation: Jordan and Diagonalization

Find the solution of the system X' using the "diagonalization" technique (actually the Jordan form in this case) Please see the attached file.

Find a solution in the form of a power series for an ODE

Please see the attached file for the fully formatted problems. Find a solution in the form of a power series for the equation y" - 2*x*y' = 0 (ie find 2 linearly independent solutions y1(x) and y2(x)). After doing that, note that the equation can also be solved directly by integration: y"/y' = 2x ln(y') = x^2 + c1 y' = ke^(x^2) k=e^c1 y = k* integral((e^(t^2))dt + C) from 0 to x Thus, one of your power series solutions gives and explicit form for the integral: integral(e^(t^2)dt) from 0 to x

Solving First Order Separable Differential Equation.

Find the solution of dy/dx-2y =0