Internal problem ID [14674]
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: 63 (c).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = -1, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.75 (sec). Leaf size: 320
dsolve([31/100*diff(y(t),t$3)+112/10*diff(y(t),t$2)-98/10*diff(y(t),t)+53/10*y(t)=0,y(0) = -1, D(y)(0) = -1, (D@@2)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\left (\left (-1228360 \sqrt {3}\, \sqrt {19889065283}+588872235000\right ) \left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {1}{3}}+\left (-1213 \sqrt {3}\, \sqrt {19889065283}-527826711\right ) \left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {2}{3}}-6259676620 \sqrt {3}\, \sqrt {19889065283}-110980984279140\right ) \cos \left (\frac {\sqrt {3}\, \left (\left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {2}{3}}-1345540\right ) t}{186 \left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {1}{3}}}\right )-527826711 \sin \left (\frac {\sqrt {3}\, \left (\left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {2}{3}}-1345540\right ) t}{186 \left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {1}{3}}}\right ) \left (\left (\frac {196290745000 \sqrt {3}}{175942237}-\frac {1228360 \sqrt {19889065283}}{175942237}\right ) \left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {1}{3}}+\left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {2}{3}} \left (\sqrt {3}+\frac {1213 \sqrt {19889065283}}{175942237}\right )\right )\right ) {\mathrm e}^{\frac {\left (1345540+\left (1564919155+465 \sqrt {59667195849}\right )^{\frac {2}{3}}-2240 \left (1564919155+465 \sqrt {59667195849}\right )^{\frac {1}{3}}\right ) t}{186 \left (1564919155+465 \sqrt {59667195849}\right )^{\frac {1}{3}}}}+1213 \,{\mathrm e}^{-\frac {\left (\left (1564919155+465 \sqrt {59667195849}\right )^{\frac {2}{3}}+1120 \left (1564919155+465 \sqrt {59667195849}\right )^{\frac {1}{3}}+1345540\right ) t}{93 \left (1564919155+465 \sqrt {59667195849}\right )^{\frac {1}{3}}}} \left (\left (\frac {1228360 \sqrt {3}\, \sqrt {19889065283}}{1213}-\frac {588872235000}{1213}\right ) \left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {1}{3}}+\left (\sqrt {3}\, \sqrt {19889065283}+\frac {527826711}{1213}\right ) \left (1564919155+465 \sqrt {3}\, \sqrt {19889065283}\right )^{\frac {2}{3}}-\frac {3129838310 \sqrt {3}\, \sqrt {19889065283}}{1213}-\frac {55490492139570}{1213}\right )}{9389514930 \sqrt {3}\, \sqrt {19889065283}+166471476418710} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 905
DSolve[{31/100*y'''[t]+112/10*y''[t]-98/10*y'[t]+53/10*y[t]==0,{y[0]==-1,y'[0]==-1,y''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]^2-e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]^2+e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]^2 \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]-e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]^2+e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]^2-e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ] \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]^2-e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]^2 \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]+e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]^2 \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]+e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]^2-e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]^2+e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ] \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]^2-e^{t \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]} \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ] \text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]^2}{\left (\text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]-\text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]\right ) \left (-\text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,1\right ]+\text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]\right ) \left (-\text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,2\right ]+\text {Root}\left [31 \text {$\#$1}^3+1120 \text {$\#$1}^2-980 \text {$\#$1}+530\&,3\right ]\right )} \]