Internal problem ID [13697]
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: 22.1 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=27 \,{\mathrm e}^{6 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=27*exp(6*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+3 \,{\mathrm e}^{6 x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 25
DSolve[y''[x]-6*y'[x]+9*y[x]==27*Exp[6*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} \left (3 e^{3 x}+c_2 x+c_1\right ) \]