75.16.38 problem 511

Internal problem ID [17011]
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 : 511
Date solved : Tuesday, January 28, 2025 at 09:45:30 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

\[ y = -\frac {c_{1} {\mathrm e}^{-2 x}}{2}-x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

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

\[ y(x)\to -x-\frac {1}{2} c_1 e^{-2 x}+c_2 \]