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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16, Problem 8PS

Textbook Problem

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Euler’s Differential Equation Euler’s differential equation is of the form

Where a and b are constants.

Show that this equation can be transformed into a second-order linear differential equation with constant coefficients by using the substitution x = e^{t}.

Solve

**(a)**

To determine

**To prove:** That the differential equation

**Given information:**

The differential equation

**Proof:**

As

Taking natural log on both the sides.

Differentiate with respect to *x*.

Now, calculate the value of

Calculate the value of

**(b)**

To determine

**To calculate:** The solution of the equation

Multivariable Calculus

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