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Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a...

Consider the differential equation y′′+ 9y′= 0.(

a) Let u=y′=dy/dt. Rewrite the differential equation as a first-order differential equation in terms of the variables u. Solve the first-order differential equation for u (using either separation of variables or an integrating factor) and integrate u to find y.

(b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution.

(c) Find the solution to the initial value problem y′′+ 9y′= 0, y(0) = 1, y′(0) = 1.

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