Internal problem ID [15383]
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. Initial value problem. Exercises page 140
Problem number: 614.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-5 y=1} \] With initial conditions \begin {align*} \left [y \left (\infty \right ) = -{\frac {1}{5}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = -\operatorname {signum}\left (c_{2} {\mathrm e}^{-\frac {\left (-1+\sqrt {21}\right ) x}{2}}\right ) \infty \]
✓ Solution by Mathematica
Time used: 0.559 (sec). Leaf size: 26
DSolve[{y''[x]-y'[x]-5*y[x]==1,{y[Infinity]==-1/5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{5}+c_1 e^{-\frac {1}{2} \left (\sqrt {21}-1\right ) x} \]