Internal problem ID [13718]
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: 22.9 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-3 \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-3*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (7 c_{2} {\mathrm e}^{7 x}+7 c_{1} +3 x \right ) {\mathrm e}^{-2 x}}{7} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 32
DSolve[y''[x]-3*y'[x]-10*y[x]==-3*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{49} e^{-2 x} \left (21 x+49 c_2 e^{7 x}+3+49 c_1\right ) \]