75.16.37 problem 510

Internal problem ID [17010]
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 : 510
Date solved : Tuesday, January 28, 2025 at 09:45:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=-2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

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

\[ y(x)\to e^{-x} \left (-2 e^x+c_2 x+c_1\right ) \]