75.16.23 problem 496

Internal problem ID [16996]
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 : 496
Date solved : Tuesday, January 28, 2025 at 09:45:20 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 33

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

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