Calc 4 basic questions Hello, can you pleasae answer all three questions? They a
ID: 3210319 • Letter: C
Question
Calc 4 basic questions
Hello, can you pleasae answer all three questions? They are really short questions so answering all questions won't take too long!
Follow the instructions on the Exam Cover Sheet for Fill-in-the Blank/Multiple Choice questions We do not solve the differential equation L[y] g(x) where L[y]y is a linear operator that maps (R,R) to (RR) by isolating the unknown function. We use the linear theory. The dimension of the null space of L[y] is 2. Since the operator L[yy +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 y c cos(x) +c, sin(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[y] (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 y, for the nonhomogeneous equation y"+ y gx): 1.(2 pts.) g(x)-2 sec(x) ABCDE 2. (2 pts.) g(x)-3 xe A BCDE 3. (2 pts.) g(x)-4x ABCDEExplanation / Answer
1. g(x)=secx C
Variation of parameters
2. g(x)=3(x^-1)(e^x) C
variation of parameter
3. g(x)=4x^2 D
both method can use