Internal problem ID [15261]
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: 491.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y=1} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {1}{6}+c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 33
DSolve[y'''[x]+6*y''[x]+11*y'[x]+6*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-3 x}+c_2 e^{-2 x}+c_3 e^{-x}+\frac {1}{6} \]