Question

Consider the following differential equation. 3x^2y'' + 6xy' + y = 0 Find all the roots of the auxiliary equation. (Enter your answers as a comma-separated list.) Solve the given differential equation. y(x) = , x > 0

          Consider the following differential equation.
3x^2y'' + 6xy' + y = 0
Find all the roots of the auxiliary equation. (Enter your answers as a comma-separated list.)
Solve the given differential equation.
y(x) = , x > 0

Added by Veronica C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Avinash Vishwakarma

04/17/2022

Step 1

Given auxiliary equation: \(3r^2 + 3r + 1 = 0\) Using the quadratic formula: \(r = \frac{-3 \pm \sqrt{3^2 - 4*3*1}}{2*3}\) Solving for \(r\), we get: \(r = -\frac{1}{2} \pm \frac{\sqrt{3}}{6}i\) Therefore, the roots of the auxiliary equation are: \(-\frac{1}{2} Show more…

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