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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16.2, Problem 4E

Textbook Problem

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Finding a General Solution Explain how to find the general solution of a higher-order homogenous linear differential equation.

To determine

**To Explain:** The procedure of a higher-order homogenous linear differential equation.

For finding the general solution of the higher order of homogeneous linear differential equation is same as that of second order equations. Now, we have to determine the n zeros of the characteristics equation. Then, based on these *n* zeros, we have formed the linear independent collections of n solutions. The major difference is that with equation of third or higher order, zeros of the characteristics solution may occur more than twice. When this happens, the linearly independent solutions are formed by multiplying by increasing powers of *x*.

**For example:**

If

Multivariable Calculus

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Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Electrical Circuit The differential equation...Ch. 16 - Investigation The differential equation...Ch. 16 - Think About It (a) Explain how, by observation,...Ch. 16 - Think About It Explain how you can find a...Ch. 16 - Power Series Solution In Exercises 59 and 60, use...Ch. 16 - Power Series Solution In Exercises 59 and 60, use...Ch. 16 - Approximation by Taylor Series In Exercises 61 and...Ch. 16 - Approximation by Taylor Series In Exercises 61 and...Ch. 16 - Finding a General Solution Find the value of k...Ch. 16 - Using an Integrating Factor The differential...Ch. 16 - Finding a General Solution Find the general...Ch. 16 - Finding a General Solution Find the general...Ch. 16 - Distinct Real Zeros Given that the characteristic...Ch. 16 - Limit of a Solution Given that a and b are...Ch. 16 - Trivial and Nontrivial Solutions Consider the...Ch. 16 - Eulers Differential Equation Eulers differential...Ch. 16 - Pendulum Consider a pendulum of length L that...Ch. 16 - Deflection of a Beam A horizontal beam with a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Airys Equation Consider Airys equation given in...Ch. 16 - ChebyshevsEquation ConsiderChebyshevs equation...Ch. 16 - Bessels Equation: Order Zero The differential...Ch. 16 - Bessels Equation: Order One The differential...Ch. 16 - Hermites Equation Consider Hermites Equation...Ch. 16 - Laguerres Equation Consider Laguerres Equation...

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