75.16.49 problem 522

Internal problem ID [17022]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 522
Date solved : Tuesday, January 28, 2025 at 09:45:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = \frac {\left (-9 x +2 c_{2} \right ) {\mathrm e}^{-3 x}}{2}+c_{1} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+3*y[x]==9*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-3 x} \left (-18 x+4 c_2 e^{2 x}-9+4 c_1\right ) \]