Internal problem ID [14645]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {5 y^{\prime \prime \prime }-15 y^{\prime }+11 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 149
dsolve(5*diff(y(t),t$3)-15*diff(y(t),t)+11*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{2} {\mathrm e}^{\frac {3 \left (\left (1100+100 \sqrt {21}\right )^{\frac {2}{3}}+100\right ) t}{20 \left (1100+100 \sqrt {21}\right )^{\frac {1}{3}}}} \sin \left (\frac {\sqrt {3}\, \left (\left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{\frac {2}{3}}-100\right ) t}{20 \left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{\frac {1}{3}}}\right )+c_{3} {\mathrm e}^{\frac {3 \left (\left (1100+100 \sqrt {21}\right )^{\frac {2}{3}}+100\right ) t}{20 \left (1100+100 \sqrt {21}\right )^{\frac {1}{3}}}} \cos \left (\frac {\sqrt {3}\, \left (\left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{\frac {2}{3}}-100\right ) t}{20 \left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{\frac {1}{3}}}\right )+c_{1} \right ) {\mathrm e}^{-\frac {\left (\left (1100+100 \sqrt {21}\right )^{\frac {2}{3}}+100\right ) t}{10 \left (1100+100 \sqrt {21}\right )^{\frac {1}{3}}}} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 75
DSolve[5*y'''[t]-15*y'[t]+11*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_2 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,2\right ]\right )+c_3 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,3\right ]\right )+c_1 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,1\right ]\right ) \]