75.18.24 problem 613

Internal problem ID [17112]
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. Initial value problem. Exercises page 140
Problem number : 613
Date solved : Tuesday, January 28, 2025 at 08:26:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \end{align*}

With initial conditions

\begin{align*} y \left (-\infty \right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.446 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)+4*diff(y(x),x)+3*y(x)=8*exp(x)+9,y(-infinity) = 3],y(x), singsol=all)
 

\[ y = -\operatorname {signum}\left (c_{2} {\mathrm e}^{-x}\right ) \infty \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],{x,2}]+4*D[y[x],x]+3*y[x]==8*Exp[x]+9,{y[-Infinity]==3}},y[x],x,IncludeSingularSolutions -> True]
 

{}