I asked ChatGPT to solve the second order linear non-homogeneous equation y"+2y+y= Is the solution that ChatGPT offers correct, or is there one or more mistakes in the work? If the work is correct, verify the solution. If it is incorrect, identify the exact place(s) where the mistake(s) occur. Explain your answer clearly! = 2x Below is the response from ChatGPT: Yes, I can solve the equation y"+2y+y = 2x. One way to solve it is to use the characteristic equation method. To find the characteristic equation, we set the left side of the equation to zero and solve for the roots of the characteristic equation, which is given by: r² + 2r + 1 = 0 Solving for the roots, we get: r₁=1+√-1-4--1+√-5 and r₂ =-1-√√-1-4 =-1-√√-5 So the roots are complex conjugates, which means the general solution of the homogeneous equation will be of the form: Yn(x) = e¯ª (c₁ cos (√5x) + c2 sin (√5 . x)) Where c₁ and c₂ are arbitrary constants. To find a particular solution, we can use the method of undetermined coefficients. Since the non- homogeneous term 2x is a polynomial of degree 1, we can assume that the particular solution is of the form: yp(x)= = ax + b Substituting this into the original equation and equating the coefficients of the like powers of a gives: a = 2 and b = 0 Therefore the particular solution is

If a projectile is launched vertically upward from the ground with an initial velocity of 90 ft per sec, neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by s= - 161" + 90t. Which equation should be used to determine the time ai which the height of the projectile reaches 20 ft? Choose the correct answer below. O A. s= - 16(20) + 90 O B. 20= - 16t +90t O C. 20= -16t Click to select wour answer 10:36 AM 2/19/202