Internal problem ID [15280]
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: 510.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=-2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=-2,y(x), singsol=all)
\[ y \left (x \right ) = -2+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 23
DSolve[y''[x]+2*y'[x]+y[x]==-2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (-2 e^x+c_2 x+c_1\right ) \]