Solve all three questions using PYTHON code

Find the values of r for which y=erx is a solution to the following differential equations. (a) y+9y+20y=0 (b) y+16y+89y=0 (c) Note the solutions in (b) are complex. Compute y+16y+89y=0 when y=e8x(cos(5x)+sin(5x)). What can you conclude about e to a complex power based on your answers to b) and c )? 2. Given the equation x3+y3=12xy : (a) Find dxdy (b) Find the points ( x and y coordinates) where the graph of the equation has a horizontal tangent line. (c) Find the points ( x and y coordinates) where the graph of the equation has a vertical tangent line. (d) Plot the graph of the equation (using plot_implicit) and the tangent lines from parts (b) and (c). Use the domain x[7.5,7.5]. 3. Given the cquation y=xe(2lim2(4x3)1/4, use logarithmic differentiation to find dxdy. (NOTE: use expand 10og on the right hand side and print your result. To see the final answer the way you would by hand, print apart (dydx/y)y, where dydx is what you obtained from logarithmic differentiation)