80.8.7 problem 7

Internal problem ID [18586]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 12:03:12 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-y&=\sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 34

dsolve(diff(y(t),t$2)+4*diff(y(t),t)-y(t)=sin(t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{\left (-2+\sqrt {5}\right ) t} c_{2} +{\mathrm e}^{-\left (2+\sqrt {5}\right ) t} c_{1} -\frac {\cos \left (t \right )}{5}-\frac {\sin \left (t \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.250 (sec). Leaf size: 47

DSolve[D[y[t],{t,2}]+4*D[y[t],t]-y[t]==Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {\sin (t)}{10}-\frac {\cos (t)}{5}+e^{-\left (\left (2+\sqrt {5}\right ) t\right )} \left (c_2 e^{2 \sqrt {5} t}+c_1\right ) \]