3.Consider the system x*=4x-y, y*=2x+y
(a) Write the system in matrix form and find the
eigenvalues and eigenvectors of the matrix A.
(b) Classify the fixed point at the origin
(c) Find the general solution of the system
(d) Solve the system subject to the initial condition
Solve the initial value problem dy/dx = −(2x cos(x^2))y +
6(x^2)e^(− sin(x^2)) , y(0) = −5
Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1
+ t^6)^2 , y(1) = 8.
Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t
A. Find the region bounded by the curves y = (x−3)^2 and y =
12−4x. Show all of your work.
B. Find the equation of the tangent line to the curve 5x^2 −6xy
+ 5y^2 = 4 at the point (1,1) Show all of your work. Thanks