20.12.6 problem Problem 21

Internal problem ID [3800]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page 575
Problem number : Problem 21
Date solved : Monday, January 27, 2025 at 08:02:29 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=\sin \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 48

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+25*diff(y(x),x)=sin(4*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (\left (3 c_{1} -4 c_{2} \right ) \cos \left (4 x \right )+4 \left (c_{1} +\frac {3 c_{2}}{4}\right ) \sin \left (4 x \right )\right ) {\mathrm e}^{3 x}}{25}+c_3 -\frac {\cos \left (4 x \right )}{292}+\frac {2 \sin \left (4 x \right )}{219} \]

✓ Solution by Mathematica

Time used: 0.699 (sec). Leaf size: 60

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+25*D[y[x],x]==Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\left (25+292 (4 c_1-3 c_2) e^{3 x}\right ) \cos (4 x)}{7300}+\frac {\left (50+219 (3 c_1+4 c_2) e^{3 x}\right ) \sin (4 x)}{5475}+c_3 \]