3. Construct a suitable Liaponov function of the form ax + by and use it to determine the type of stability of the origin in each of the following systems: dx dx = 3x'y' - x' dt (b) dy =x' + 3x*y' dt = y' - 3x'y dt =-3x'y² - y' dt

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A: B.

Q: 16 Q4- Solve the following system of ODE dx dt Eaux"> dy dt = y + 1 =x+1

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.