Internal problem ID [13702]
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 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=25 \sin \left (6 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=25*sin(6*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+\frac {4 \cos \left (6 x \right )}{9}-\frac {\sin \left (6 x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 35
DSolve[y''[x]-6*y'[x]+9*y[x]==25*Sin[6*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{3} \sin (6 x)+\frac {4}{9} \cos (6 x)+e^{3 x} (c_2 x+c_1) \]