75.18.25 problem 614

Internal problem ID [17113]
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 : 614
Date solved : Tuesday, January 28, 2025 at 09:53:18 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=-{\frac {1}{5}} \end{align*}

✓ Solution by Maple

Time used: 0.339 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)-diff(y(x),x)-5*y(x)=1,y(infinity) = -1/5],y(x), singsol=all)
 

\[ y = -\operatorname {signum}\left (c_{2} {\mathrm e}^{-\frac {\left (-1+\sqrt {21}\right ) x}{2}}\right ) \infty \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 26

DSolve[{D[y[x],{x,2}]-D[y[x],x]-5*y[x]==1,{y[Infinity]==-1/5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{5}+c_1 e^{-\frac {1}{2} \left (\sqrt {21}-1\right ) x} \]