Internal problem ID [13728]
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: 22.10 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=8 \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=8*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} +4 \,{\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 29
DSolve[y''[x]+4*y'[x]+5*y[x]==8*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (c_2 e^x \cos (x)+c_1 e^x \sin (x)+4\right ) \]