Compute the linearized IVP system for the IVP system dx/dt = y-(x2+y2)x, x(0)=1 dy/dt= -x-(x2+y2)y, y(0)=0 Solution For the first part we will place 0 in place of x as following and will consider whole equation equal to 1 So dx/dt = y-(x2+y2)x 1 = y - (x2+y2)*0 Ans :: Y=1 Similarly for the second we will place y=o and assume whole equation equal to 0 So, dy/dt= -x-(x2+y2)y 0 = -x- 0 Ans:: x=0.

1. Compute the linearized IVP system for the IVP system
dx/dt = y-(x2+y2)x, x(0)=1
dy/dt= -x-(x2+y2)y, y(0)=0
Solution
For the first part we will place 0 in place of x as following and will consider whole
equation equal to 1 So dx/dt = y-(x2+y2)x 1 = y - (x2+y2)*0 Ans :: Y=1 Similarly for the
second we will place y=o and assume whole equation equal to 0 So, dy/dt= -x-(x2+y2)y 0 = -x-
0 Ans:: x=0