68.11.41 problem 53

Internal problem ID [17578]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 53
Date solved : Thursday, October 02, 2025 at 02:25:39 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {1}{25}} \\ y^{\prime }\left (0\right )&=7 \\ \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 16

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+25*y(t) = -1; 
ic:=[y(0) = -1/25, D(y)(0) = 7]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {7 \,{\mathrm e}^{-3 t} \sin \left (4 t \right )}{4}-\frac {1}{25} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 22

ode=D[y[t],{t,2}]+6*D[y[t],t]+25*y[t]==-1; 
ic={y[0]==-1/25,Derivative[1][y][0] ==7}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {7}{4} e^{-3 t} \sin (4 t)-\frac {1}{25} \end{align*}

✓ Sympy. Time used: 0.137 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)) + 1,0) 
ics = {y(0): -1/25, Subs(Derivative(y(t), t), t, 0): 7} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {1}{25} + \frac {7 e^{- 3 t} \sin {\left (4 t \right )}}{4} \]