9. For the differential equation: ?′′ + 2?′ + 5? = ?(?) (a) Write down the...

9. For the differential equation: ?′′ + 2?′ + 5? = ?(?)

(a) Write down the auxiliary polynomial associated to this differential equation and find the roots of the auxiliary polynomial.

(b) Find a basis for the real solution set of the associated homogeneous differential equation ?′′ + 2?′ + 5? = 0.

(c) For each ?(?) that follows, write down the trial particular solution to ?′′ + 2?′ + 5? = ?(?), with undetermined coefficients. Do NOT solve the constants that arise in your trial solution.

(i) ?(?) = 120?^−?

(ii) ??(??) = 68 cos(2?)

(iii) ??(??) = 3?

(iv) ??(??) = 75?^−? sin(2?)

(d) Find a particular solution to ?′′ + 2?′ + 5? = 100 cos(2?) (show your work)

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not...

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not exact. (b) Find a value for the constant a such that, when you multiply the d.e. through by xa, it becomes exact. Show your working. Do NOT solve the resulting differential equation. 6. Consider the differential equation (D − 3)(D − 4)y = 0. (a) Solve this d.e., showing brief working. (b) How many solutions does this d.e. have? Justify your answer. (c) How...

5. (a) Write down the Bernoulli’s equation and the continuity equation. (b) The entry and exit...

5. (a) Write down the Bernoulli’s equation and the continuity equation. (b) The entry and exit mouths of an uneven water pipe have areas of 0.2 m2 and 0.05 m2, respectively. If water enters the pipe at a speed of 5m/s find the speed of water exiting the pipe.

1. What is a differential? 2. What is a differential equation?

1. What is a differential? 2. What is a differential equation? 3. Besides the fact that you might need the course to graduate, how might differential equations be useful to you in real life?

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most

write a differential equation that describes the following: a mass weighing 12lb stretches a spring 2...

write a differential equation that describes the following: a mass weighing 12lb stretches a spring 2 ft. the mass is initially released from a point 1 ft below the equilibrium position with an upward velocity of 4 ft/s. (gravity is 32 ft/s^2) 1. find the equation of motion, what are the natural circular frequency, period and amplitude 2. at what time does the mass return 1 foot below the equilibrium position 3. at what time does the mass pass through...

5 solved examples for (differential equation in fluid dynamics )

5 solved examples for (differential equation in fluid dynamics ) *the exampls (proplems) should be have differential equation in Operative of the question (It is preferable to be for the highest order) and The answer should be a solution to these differential equations

Question