Math 554 homework - use matlab to solve the following

Question

Use Matlab to solve the following equations. Please (i) plot the solution as a function of t for t  ∈ [0, 100].

(ii) draw the phase diagram of the ODE.

1. dy/dt = y² + y with y(0) = 1

 

      dy₁/dt = y₂

2.                                         with y₁(0) = 1, y₂(0) = 1.

      dy₂/dt = -3y₂ + 2y₁

 

       dy₁/dt = y₁ - 2y₁y₂

3.                                         with y₁(0) = 1, y₂(0) = 1.

       dy₂/dt = -y₁y₂ - y₂

 

    dy₁/dt = -y₁y₂

4. dy₂/dt = y₁y₂ - y₂ with y₁(0) = 10, y₂(0) = 1, y₃ = 0.

    dy₃/dt = y₂