80.8.9 problem 10

Internal problem ID [18588]
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 : 10
Date solved : Tuesday, January 28, 2025 at 12:03:20 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 5 x^{\prime }+x&=\sin \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(5*diff(x(t),t)+x(t)=sin(3*t),x(t), singsol=all)
 

\[ x = -\frac {15 \cos \left (3 t \right )}{226}+\frac {\sin \left (3 t \right )}{226}+{\mathrm e}^{-\frac {t}{5}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 31

DSolve[5*D[x[t],t]+x[t]==Sin[3*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{226} (\sin (3 t)-15 \cos (3 t))+c_1 e^{-t/5} \]