73.15.8 problem 22.3 (c)

Internal problem ID [15439]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.3 (c)
Date solved : Tuesday, January 28, 2025 at 07:55:46 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+3*diff(y(x),x)=26*cos(x/3)-12*sin(x/3),y(x), singsol=all)
 

\[ y = -\frac {c_{1} {\mathrm e}^{-3 x}}{3}+27 \sin \left (\frac {x}{3}\right )+9 \cos \left (\frac {x}{3}\right )+c_{2} \]

✓ Solution by Mathematica

Time used: 6.548 (sec). Leaf size: 60

DSolve[D[y[x],{x,2}]+3*D[y[x],x]==26*Cos[x/3]-12*Sin[x/3],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-3 K[2]} \left (c_1+\int _1^{K[2]}2 e^{3 K[1]} \left (13 \cos \left (\frac {K[1]}{3}\right )-6 \sin \left (\frac {K[1]}{3}\right )\right )dK[1]\right )dK[2]+c_2 \]