Internal problem ID [13416]
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 (n).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=6 \cos \left (2 x \right )-3 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=6*cos(2*x)-3*sin(2*x),y(x), singsol=all)
\[ y = c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )-2 \cos \left (2 x \right )+\sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 26
DSolve[y''[x]+y[x]==6*Cos[2*x]-3*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (2 x)-2 \cos (2 x)+c_1 \cos (x)+c_2 \sin (x) \]