75.16.43 problem 516

Internal problem ID [17016]
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 : 516
Date solved : Tuesday, January 28, 2025 at 09:45:36 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \end{align*}

✓ Solution by Maple

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

dsolve(3*diff(y(x),x$4)+diff(y(x),x$3)=2,y(x), singsol=all)
 

\[ y = \frac {x^{3}}{3}+\frac {c_{2} x^{2}}{2}-27 \,{\mathrm e}^{-\frac {x}{3}} c_{1} +c_{3} x +c_4 \]

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 36

DSolve[3*D[y[x],{x,4}]+D[y[x],{x,3}]==2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3}{3}+c_4 x^2+c_3 x-27 c_1 e^{-x/3}+c_2 \]