Internal problem ID [15285]
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: 515.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }=-6} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)=-6,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{6 x} c_{1}}{216}+\frac {x^{3}}{6}+\frac {c_{2} x^{2}}{2}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 36
DSolve[y''''[x]-6*y'''[x]==-6,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{6}+c_4 x^2+c_3 x+\frac {1}{216} c_1 e^{6 x}+c_2 \]