Internal problem ID [13517]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=10 \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=10*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-3 x} c_{2} +{\mathrm e}^{-3 x} x c_{1} +5 x^{2} {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 23
DSolve[y''[x]+6*y'[x]+9*y[x]==10*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (5 x^2+c_2 x+c_1\right ) \]