90.15.6 problem 6

Internal problem ID [25253]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 251
Problem number : 6
Date solved : Thursday, October 02, 2025 at 11:59:22 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=\sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)-10*y(t) = sin(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-5 t} c_2 +{\mathrm e}^{2 t} c_1 -\frac {3 \cos \left (t \right )}{130}-\frac {11 \sin \left (t \right )}{130} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 35

ode=D[y[t],{t,2}]+3*D[y[t],{t,1}]-10*y[t]==Sin[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^{-5 t}+c_2 e^{2 t}+\frac {1}{130} (-11 \sin (t)-3 \cos (t)) \end{align*}

✓ Sympy. Time used: 0.056 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-10*y(t) - sin(t) + 4*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- \frac {\sqrt {10} t}{2}} + C_{2} e^{\frac {\sqrt {10} t}{2}} - \frac {\sin {\left (t \right )}}{14} \]