Please make sure you choose the right answer What is the longest interval on whi

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Please make sure you choose the right answer

What is the longest interval on which the solution to the initial value problem ( t - l ) y - 3ty + 4y = ln | t + 5 |, y(0) = -1010, y (0) = 123 is creation to exist? ( - infinity, - 5 ) (- infinity, 1 ) (- 5, 0 ) (- 5, 1 ) (- 5. infinity ) ( 0, 1 ) ( 0. infinity ) ( 1, infinity ) Which of the following applies to the differential equation 3y + x4 = y 7 + y - cos ( x ) ? The equation is nonlinear. The equation is linear, homogeneous, with constant coefficients. The equation is linear, homogeneous, with nonconstant coefficients. The equation is linear, nonhomogeneous. with constant coefficients. The equation is linear, nonhomogeneous. with nonconstant coefficients. Which of the following applies to the differential equation y tan x = cos ( x ) y + 3 ? The equation is nonlinear. The equation is linear, nonhomogeneous. with constant coefficients. The equation is linear, nonhomogeneous. with nonconstant coefficients. The equation is linear, homogeneous, with constant coefficients. The equation is linear, homogeneous, with nonconstant coefficients. Which of the following is a Wronskian determinant W(phi1, phi2) of two linearly independent solutions phi 1 and phi 2 of the differential equation t2y -ty -3y = 0, t Greater-Than 0 ? 0 c 1 t 3 + c 2 t - 1 for some constants c 1 and c 2 . c 1 e 3 t + c 2 e - t for some constants c 1 and c 2 . c e t for some constant c . c t -1 for some constant c . c t - 1 for some constant c . c t - 1 for some constant c . There is not enough information to determine the solution. If f and g are differentiable functions on the real numbers and let I be an open interval I, which of the following statements is true? If f and g are linearly independent, then W(f , g)(to) Not Equal 0 for some to in I . If f and g are linearly independent on I , then W (f , g) (to) Not Equal 0 for all point to in I. If W(f , g) (to) = 0 for some point to in I,. then f and g are linearly dependent on I . If W(f , g) (to) = 0 for all points to on I,. then f and g are linearly dependent. all of the above are correct None of the above is correct. For all values of p and q, the differential equation y - 3y - 4y = 5 sin (pt) + 7eqt has a particular solution of the form c: cos (pt) + c2 sin (pt) + C3eqt. true false The particular solution to the differential equation 2y + 3y + y = te - t + e: cos t has the form . . . y = c 2 t e -t + c 3 e : cos t. y = (c 1 t + c 2 ) e - t + c 3 e t cos t. y = ( c : t - c 2 ) e - t + e t (c 3 cos t + c 4 sin t). y = (c 1 t + c 2) e - t + c 3 e t cos t. y = ( c 1 t 3 + c 2 t ) e t(c 3 cos t + c 4 sin t). Following is a graph of the solution to the initial value problem: a 0 y + a 1 y + a 2 = 0, y ( 0 ) = c 0 , y ( 0 ) = c 1. From the graph, what can we conclude about the roots of the characteristic equation? (You may assume that graph gives enough information for you to infer the global properties of the function.) complex, real part is positive complex, real part is zero complex, real part is negative both real and positive both real and negative both real and have differing signs Following is a graph of the solution to the initial value problem a 0 y + a 1 y + a 2 =0, y (0) = c 1, y (0) = c 1. From the graph, what can we conclude about the roots of the characteristic equation? (You may assume that graph gives enough information for you to infer the global properties of the function.)..complex, real part is positive complex, real part is negative both real and positive both real and negative both real and have differing signs

Explanation / Answer

1).d

2).d

3).a

4).c

5).e

6).a

7).e

8).c

9).c

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