Internal problem ID [13407]
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: 22.10 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=24 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=24*sin(3*x),y(x), singsol=all)
\[ y = {\mathrm e}^{-2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} -\frac {3 \sin \left (3 x \right )}{5}-\frac {9 \cos \left (3 x \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 41
DSolve[y''[x]+4*y'[x]+5*y[x]==24*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {3}{5} (\sin (3 x)+3 \cos (3 x))+c_2 e^{-2 x} \cos (x)+c_1 e^{-2 x} \sin (x) \]