74.13.9 problem 26

Internal problem ID [16375]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 09:07:19 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime \prime }-15 y^{\prime }+11 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 149

dsolve(5*diff(y(t),t$3)-15*diff(y(t),t)+11*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{\frac {3 \left (\left (1100+100 \sqrt {21}\right )^{{2}/{3}}+100\right ) t}{20 \left (1100+100 \sqrt {21}\right )^{{1}/{3}}}} \sin \left (\frac {\sqrt {3}\, \left (\left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{2}/{3}}-100\right ) t}{20 \left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{1}/{3}}}\right )+c_{3} {\mathrm e}^{\frac {3 \left (\left (1100+100 \sqrt {21}\right )^{{2}/{3}}+100\right ) t}{20 \left (1100+100 \sqrt {21}\right )^{{1}/{3}}}} \cos \left (\frac {\sqrt {3}\, \left (\left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{2}/{3}}-100\right ) t}{20 \left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{1}/{3}}}\right )+c_{1} \right ) {\mathrm e}^{-\frac {\left (\left (1100+100 \sqrt {21}\right )^{{2}/{3}}+100\right ) t}{10 \left (1100+100 \sqrt {21}\right )^{{1}/{3}}}} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 75

DSolve[5*D[ y[t],{t,3}]-15*D[y[t],t]+11*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_2 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,2\right ]\right )+c_3 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,3\right ]\right )+c_1 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,1\right ]\right ) \]