B) False

2.) If $\phi$ is a solution to a first order linear homogeneous differential equation, then $c\phi$ is also a solution to this equation.

                   A) True                    

3.) If $\phi$ is a solution to a first order linear homogeneous differential equation with constant coefficients, then $c\phi$ is also a solution to this equation.

                   A) True                    

1.) If $b^2 - 4ac < 0$ then the solution to the initial value problem $ay'' + by' + cy = 0$, $y(0) = -1$, $y'(0) = -3$ is complex valued.

                                        B) False

657688

2.) If $b^2 - 4ac < 0$ then the solution to the initial value problem $ay'' + by' + cy = 0$, $y(0) = -1$, $y'(0) = -3$ is real valued.

                   A) True 657689                    

1.) $L(g) = g'' + p(t) g' + q(t)g$ is a linear function on the space of all twice differentiable functions.

                   A) True 672134            

2.) $L(g) = g'' + p(t) g' + q(t)gg'$ is a linear function on the space of all twice differentiable functions.

                                B) False

672137

1.) There is a unique solution to the differential equation ay'' + by + cy = g(t), y(0) = 1, y'(0) = 3

                   A) True 734194            

2.) There is a unique solution to the differential equation ay'' + by + cy = g(t), y(0) = 1, y(1) = 3

                                B) False

4

3.) There is a unique solution to the differential equation ay'' + by + cy = g(t), y(0) = 1, y'(1) = 3

                                B) False

734216

4.) There is a unique solution to the differential equation ay'' + by + cy = g(t), y(1) = 1, y'(1) = 3

                   A) True 7            

1.) When taking the derivative with respect to $t$, $(y^2)' = 2y$

                                B) False

2.) When taking the derivative with respect to $t$, $(y^2)' = 2yy'$

                   A) True            

3.) If $y(0) = -2$ and $y^2 = g(t)$, then $y(t) = \sqrt{g(t)}$

                                B) False

4.) If $y(0) = -2$ and $y^2 = g(t)$, then $y(t) = -\sqrt{g(t)}$

                   A) True