75.16.42 problem 515

Internal problem ID [17015]
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 : 515
Date solved : Tuesday, January 28, 2025 at 09:45:36 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)=-6,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{6 x} c_{1}}{216}+\frac {x^{3}}{6}+\frac {c_{2} x^{2}}{2}+c_{3} x +c_4 \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 36

DSolve[D[y[x],{x,4}]-6*D[y[x],{x,3}]==-6,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3}{6}+c_4 x^2+c_3 x+\frac {1}{216} c_1 e^{6 x}+c_2 \]