Question

Find y(1), if x(t), y(t), and z(t) are solutions of the system:

x'=x+3y
y'=x-y
z'=3z

satisfying the initial conditions x(0)=y(0)=z(0)=2.

Can you solve and explain your steps?

Answer 1

System is here:

http://www.wolframalpha.com/input/?i=x%27%3Dx%2B3y%2C+y%27%3Dx-y%2C+z%27%3D3z

Make the necessary substitutions to find the constants given the initial conditions, then solve y(1).