75.16.18 problem 491

Internal problem ID [16991]
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 : 491
Date solved : Tuesday, January 28, 2025 at 09:45:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

dsolve(diff(y(x),x$3)+6*diff(y(x),x$2)+11*diff(y(x),x)+6*y(x)=1,y(x), singsol=all)
 

\[ y = \frac {1}{6}+c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 33

DSolve[D[y[x],{x,3}]+6*D[y[x],{x,2}]+11*D[y[x],x]+6*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-3 x}+c_2 e^{-2 x}+c_3 e^{-x}+\frac {1}{6} \]