Internal problem ID [13383]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right )} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.29 (sec). Leaf size: 35
DSolve[y''[x]+3*y'[x]==26*Cos[x/3]-12*Sin[x/3],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 27 \sin \left (\frac {x}{3}\right )+9 \cos \left (\frac {x}{3}\right )-\frac {1}{3} c_1 e^{-3 x}+c_2 \]