exercise:F045eb2a12: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow}...") |
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<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li> | ||
Show that <math>y = c_1e^{\alpha x}\sin(\beta x+c_2)</math> | Show that <math>y = c_1e^{\alpha x}\sin(\beta x+c_2)</math> | ||
is a solution of the differential equation | is a solution of the differential equation | ||
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<li>Show that <math>y = c_1e^{\alpha x}\cos(\beta x+c_2)</math> | <li>Show that <math>y = c_1e^{\alpha x}\cos(\beta x+c_2)</math> | ||
is also a solution of the differential equation | is also a solution of the differential equation | ||
in | in (a).</li> | ||
</ul> | </ul> | ||
Latest revision as of 02:02, 24 November 2024
[math]
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[/math]
- Show that [math]y = c_1e^{\alpha x}\sin(\beta x+c_2)[/math] is a solution of the differential equation [math]y^{\prime\prime} - 2\alpha y^\prime + (\alpha^2+\beta^2)y = 0[/math].
- Show that [math]y = c_1e^{\alpha x}\cos(\beta x+c_2)[/math] is also a solution of the differential equation in (a).