0
answers
0
watching
195
views
6 Nov 2019
Consider the differential equation (D + 3)y = 7. (Here, D denotes differentiation with respect to time t *) Is y = c1e-3t + 4 a general solution? Identify what part of y prevents it from being a solution. Define y* = c1e-3t + c2. Determine specific values of c1 and c2 so that y* is a general solution. Hint. Do not "solve" the equation - instead use the definition of solution in both of these problems. For the homogeneous equation (x2 + y2)dx + 0 make the substitution y = ux at produce an equation in which variables u and x are separated. No additional work is required. * This is an example of differential operator notation. Literally, (D + 3)y means Dy + 3y which is equivalent dy/dt + 3y. Show transcribed image text
Consider the differential equation (D + 3)y = 7. (Here, D denotes differentiation with respect to time t *) Is y = c1e-3t + 4 a general solution? Identify what part of y prevents it from being a solution. Define y* = c1e-3t + c2. Determine specific values of c1 and c2 so that y* is a general solution. Hint. Do not "solve" the equation - instead use the definition of solution in both of these problems. For the homogeneous equation (x2 + y2)dx + 0 make the substitution y = ux at produce an equation in which variables u and x are separated. No additional work is required. * This is an example of differential operator notation. Literally, (D + 3)y means Dy + 3y which is equivalent dy/dt + 3y.
Show transcribed image text