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Math  /  Calculus

Question1,2,3,4,51,2,3,4,5, and 6 Specify whether each system is autonomous or nonautonomous, and whether it is linear or nonlinear. If it is linear, specify whether it is homogeneous or nonhomogeneous.
1. dx/dt=x−y,dy/dt=−3ty+xd x / d t=x-y, \quad d y / d t=-3 t y+x
HIDE ANSWER Answer: Linear, homogeneous, nonautonomous
2. dy/dx=2y,dz/dx=x−z+3d y / d x=2 y, d z / d x=x-z+3
3. dy/dt=3yz−2z,dz/dt=2z+5yd y / d t=3 y z-2 z, \quad d z / d t=2 z+5 y

Studdy Solution
Analyze the system to determine if it is linear.
- The first equation contains a product of variables 3yz 3yz , which is nonlinear.
The system is nonlinear.
For the third system, the classification is: Nonlinear, autonomous.

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