Internal problem ID [13726]
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 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=6 \,{\mathrm e}^{-5 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=6*exp(-5*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{5 x}+\frac {3 \,{\mathrm e}^{-5 x}}{50} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 28
DSolve[y''[x]-10*y'[x]+25*y[x]==6*Exp[-5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 e^{-5 x}}{50}+e^{5 x} (c_2 x+c_1) \]