Internal problem ID [13415]
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 (m).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=6 \cos \left (x \right )-3 \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+y(x)=6*cos(x)-3*sin(x),y(x), singsol=all)
\[ y = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )+3 \cos \left (x \right )+3 x \sin \left (x \right )+\frac {3 x \cos \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 27
DSolve[y''[x]+y[x]==6*Cos[x]-3*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\frac {3 x}{2}+3+c_1\right ) \cos (x)+(3 x+c_2) \sin (x) \]