Internal problem ID [13395]
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: 22.7 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=(-6*x-8)*cos(2*x)+(8*x-11)*sin(2*x),y(x), singsol=all)
\[ y = {\mathrm e}^{x} c_{2} +x \,{\mathrm e}^{x} c_{1} +\sin \left (2 x \right )+2 x \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 28
DSolve[y''[x]-2*y'[x]+y[x]==(-6*x-8)*Cos[2*x]+(8*x-11)*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (2 x)+2 x \cos (2 x)+e^x (c_2 x+c_1) \]