40.9.4 problem 14

Internal problem ID [6714]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:24:40 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=5 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x$5)-4*diff(y(x),x$3)=5,y(x), singsol=all)
 

\[ y = -\frac {5 x^{3}}{24}+\frac {c_2 \,{\mathrm e}^{2 x}}{8}+\frac {c_3 \,x^{2}}{2}-\frac {{\mathrm e}^{-2 x} c_1}{8}+c_4 x +c_5 \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 47

DSolve[D[y[x],{x,5}]-4*D[y[x],{x,3}]==5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {5 x^3}{24}+c_5 x^2+c_4 x+\frac {1}{8} c_1 e^{2 x}-\frac {1}{8} c_2 e^{-2 x}+c_3 \]