68.13.38 problem 63 (c)

Internal problem ID [17691]
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)
Date solved : Thursday, October 02, 2025 at 02:27:04 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} \frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}&=0 \end{align*}

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*}

✓ Maple. Time used: 0.801 (sec). Leaf size: 326

ode:=31/100*diff(diff(diff(y(t),t),t),t)+56/5*diff(diff(y(t),t),t)-49/5*diff(y(t),t)+53/10*y(t) = 0; 
ic:=[y(0) = -1, D(y)(0) = -1, (D@@2)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 905

ode=31/100*D[ y[t],{t,3}]+112/10*D[y[t],{t,2}]-98/10*D[y[t],t]+53/10*y[t]==0; 
ic={y[0]==-1,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(53*y(t)/10 - 49*Derivative(y(t), t)/5 + 56*Derivative(y(t), (t, 2))/5 + 31*Derivative(y(t), (t, 3))/100,0) 
ics = {y(0): -1, Subs(Derivative(y(t), t), t, 0): -1, Subs(Derivative(y(t), (t, 2)), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out