Textbook Problem

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Motion of a Spring In Exercise 55-58, match the differential equation with the graph of a particular solution. [The graphs are labeled (a), (b), (c) and (d).] The correct match can be made by comparing the frequency of the oscillations or the rate at which the oscillations are being damped with the appropriate coefficient in the differential equation.

$y^{″}+2y^{\prime }+10y=0$

To determine

The graph of the particular solution of the differential equation $y^{″}+2y^{\prime }+10y=0$.

Explanation of Solution

Given information: The graphs,

Comparing the equation $y^{″}+2y^{\prime }+10y=0$ with the standard equation $a{y}^{″}+b{y}^{\prime }+cy=0$ to get $a=1,b=2,\text{and}c=10$