Internal problem ID [15292]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 522.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+3 y=9 \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+3*y(x)=9*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-9 x +2 c_{2} \right ) {\mathrm e}^{-3 x}}{2}+c_{1} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 32
DSolve[y''[x]+4*y'[x]+3*y[x]==9*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-3 x} \left (-18 x+4 c_2 e^{2 x}-9+4 c_1\right ) \]