Calculs 4 Question Hello, Can you solve all the questions. You don\'t actually h

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Calculs 4 Question

Hello, Can you solve all the questions. You don't actually have to solve it it's just picking the correct method so it wouldnt take more than a minute

Follow the instructions on the Exam Cover Sheet for Fill-in-the Blank/Multiple Choice questions. The dimension of the null space of the linear operator L[y] y" + y that maps(R,R) to (R,R) is 2. Since the operator L[y y" + y has constant coefficients, we assume a solution of the homogeneous equation L[y 0 of the form y-e. This leads to the two linearly independent solutions y cos(x) and y2 sin(x) so that a basis of the nullspace of L is B-{cos(x), sin(x)). Hence we can deduce that ye-ci cos(x) + , sm(X) is the general solution of the homogeneous equation y" + y-0 To use the linear theory to obtain the general solution of the nonhomogeneous equation L[yl -g(x), we need a particular solution, yp, to y" y g(x). We have studied two techniques for this purpose (attendance is required) i) Undetermined Coefficients (also called judicious guessing) ii) Variation of Parameters (also called variation of constants) For each of the functions g(x) given below, circle the correct answer that describes which of these techniques can be used to find yp for the nonhomogeneous equation y" ty g(x) 1. (2 pts.) g(x)- 3*(e x) 2. (2 pts.) g(x)-e 3. (2 pts.) gx)n (x) ABCDE ABCDE ABCDE A) Neither technique works to find yp B) Only Undetermined Coefficients works to find yp C) Only Variation of Parameters works to find yp D) Either technique works to find yp E) Not enough information is given. AB) Too much information is given. AC) All of the above statements are true AD) None of the above statements are true

Explanation / Answer

1) Answer is D

Both the methods (techniques) works to find yp

2)Answer is D

Both the methods (techniques) works to find yp

3)Answer is C

only variation of parameter methods will works to find yp

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