Internal problem ID [13741]
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: 22.11 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=4 \,{\mathrm e}^{-8 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=4*exp(-8*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-8 x} \left ({\mathrm e}^{10 x} c_{1} +c_{2} {\mathrm e}^{11 x}+\frac {2}{55}\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 31
DSolve[y''[x]-5*y'[x]+6*y[x]==4*Exp[-8*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 e^{-8 x}}{55}+c_1 e^{2 x}+c_2 e^{3 x} \]