Question

Two solutions to a second order differential equation are linearly independent if (a) their Wronskian determinant is zero. (b) their Wronskian determinant is nonzero. (c) they are not scalar multiples of one another. (d) they each have a corresponding initial condition. (e) Both (b) and (c) are correct. Given the differential equation y"+9y' = e-91, the correct guess for a particular solution would be (a) yp = Ae-94 (b) yp = (Ax + B)e-9r. (c) yp = A + Be-92 (d) yp = Axe-9x (e) None of the above are correct. In which situation should Variation of Parameters be used as opposed to Un- determined Coefficients? (a) If the forcing function is secr. (b) If the forcing function is linearly dependent on part of the homogeneous solution. (c) If the differential equation is homogeneous. (d) If there is a procedure for guessing the particular solution. (e) When the Wronskian is nonzero.

3 multiple choice questions

Answer 1

benicarly. Tune solution to a second order differential equation are dependent if (6) their wronkian determinant they are not scalar multiple of one another (e) poth (6) & (C) are correct non zero co

and determined coefficu sub corred Given the differential equation que cabe pantalar Solution 9x P90 9x D + 1 (- 9) e D-9 .-9x.e -9x Axe-x. √ (d) up In which situation should variation parameter le used as opposed to (b) the forcing function is linearly dependent part of the homogen If solution