81.5.14 problem 14

Internal problem ID [18677]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 58
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 12:09:19 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

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

\[ y \left (x \right ) = -x^{4}-24+\cos \left (x \right ) c_{1} +c_{2} {\mathrm e}^{x}+c_3 \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

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

\[ y(x)\to -x^4+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x)-24 \]