30.12.35 problem 45 (a)

Internal problem ID [7627]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 45 (a)
Date solved : Tuesday, September 30, 2025 at 04:55:06 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }+18 y^{\prime \prime }+13 y^{\prime }-19 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 136

ode:=3*diff(diff(diff(y(t),t),t),t)+18*diff(diff(y(t),t),t)+13*diff(y(t),t)-19*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_3 \,{\mathrm e}^{\frac {t \left (\left (-108+4 i \sqrt {47939}\right )^{{2}/{3}}+92\right )}{4 \left (-108+4 i \sqrt {47939}\right )^{{1}/{3}}}}+c_1 \,{\mathrm e}^{-\frac {i t \sqrt {3}\, \left (\left (-108+4 i \sqrt {47939}\right )^{{2}/{3}}-92\right )}{12 \left (-108+4 i \sqrt {47939}\right )^{{1}/{3}}}}+c_2 \,{\mathrm e}^{\frac {i t \sqrt {3}\, \left (\left (-108+4 i \sqrt {47939}\right )^{{2}/{3}}-92\right )}{12 \left (-108+4 i \sqrt {47939}\right )^{{1}/{3}}}}\right ) {\mathrm e}^{-\frac {t \left (\left (-108+4 i \sqrt {47939}\right )^{{2}/{3}}+24 \left (-108+4 i \sqrt {47939}\right )^{{1}/{3}}+92\right )}{12 \left (-108+4 i \sqrt {47939}\right )^{{1}/{3}}}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 93

ode=3*D[y[t],{t,3}]+18*D[y[t],{t,2}]+13*D[y[t],{t,1}]-19*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_3 \exp \left (t \text {Root}\left [3 \text {$\#$1}^3+18 \text {$\#$1}^2+13 \text {$\#$1}-19\&,3\right ]\right )+c_2 \exp \left (t \text {Root}\left [3 \text {$\#$1}^3+18 \text {$\#$1}^2+13 \text {$\#$1}-19\&,2\right ]\right )+c_1 \exp \left (t \text {Root}\left [3 \text {$\#$1}^3+18 \text {$\#$1}^2+13 \text {$\#$1}-19\&,1\right ]\right ) \end{align*}

✓ Sympy. Time used: 6.231 (sec). Leaf size: 1834

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-19*y(t) + 13*Derivative(y(t), t) + 18*Derivative(y(t), (t, 2)) + 3*Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \text {Solution too large to show} \]