75.16.1 problem 474

Internal problem ID [16974]
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 : 474
Date solved : Tuesday, January 28, 2025 at 09:43:58 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=3 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(diff(y(x),x$2)+3*diff(y(x),x)=3,y(x), singsol=all)
 

\[ y = -\frac {c_{1} {\mathrm e}^{-3 x}}{3}+x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+3*D[y[x],x]==3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x-\frac {1}{3} c_1 e^{-3 x}+c_2 \]