15.15.5 problem 5

Internal problem ID [3209]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 5
Date solved : Monday, January 27, 2025 at 07:26:09 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 42

dsolve(diff(y(x),x$5)+diff(y(x),x$4)=x^2,y(x), singsol=all)
 

\[ y = \frac {x^{6}}{360}+\frac {x^{4}}{12}-\frac {x^{5}}{60}+\frac {c_3 \,x^{2}}{2}+\frac {c_2 \,x^{3}}{6}+{\mathrm e}^{-x} c_{1} +c_4 x +c_5 \]

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 53

DSolve[D[y[x],{x,5}]+D[y[x],{x,4}]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^6}{360}-\frac {x^5}{60}+\frac {x^4}{12}+c_5 x^3+c_4 x^2+c_3 x+c_1 e^{-x}+c_2 \]