Question

solve

x'=x

y'=-4x+2y

Answer 1

First equation is variable seperable. So we can easily get solution of this equation.

After puting value of x in second equation, it becomes linear differential equation in variable y. So find integrating factor . And now you can get solution of this equation easily.

So, solutions are:

x = c₁e^t

y = 4c₁e^t + c₂e^2t

where c₁ and c₂ are constants and x and y are functions of variable t. (Assumed)