Internal problem ID [13445]
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: 22.14 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=27*exp(6*x)+25*sin(6*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{3 x}+x \,{\mathrm e}^{3 x} c_{1} +3 \,{\mathrm e}^{6 x}+\frac {4 \cos \left (6 x \right )}{9}-\frac {\sin \left (6 x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.409 (sec). Leaf size: 42
DSolve[y''[x]-6*y'[x]+9*y[x]==27*Exp[6*x]+25*Sin[6*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{3} \sin (6 x)+\frac {4}{9} \cos (6 x)+e^{3 x} \left (3 e^{3 x}+c_2 x+c_1\right ) \]