Consider the nonhomogeneous equation: y" + by' + y = g(æ) %3D where b is a real constant. The following questions refer to your guess for Yp using the method of undetermined coefficients. Do not solve for the coefficients. (a) If g(x) = 3x – 1, what is the first guess for y,? (b) Identify the value of b if g(x) = 7 sin x and you need your second guess for Yp. What is that guess? (c) Identify the value of b if g(x) = 18e" and you need your third guess for Yp. What is that guess? (d) Explain why you will never need more than three guesses.

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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.