82.33.15 problem Ex. 15

Internal problem ID [18908]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 15
Date solved : Tuesday, January 28, 2025 at 12:34:14 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 55

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

\[ y \left (x \right ) = \frac {c_3 \sin \left (a x \right ) a^{8}+\cos \left (a x \right ) c_{1} a^{8}+c_{2} {\mathrm e}^{a x} a^{8}+c_4 \,{\mathrm e}^{-a x} a^{8}-x^{4} a^{4}-24}{a^{8}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 51

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

\[ y(x)\to -\frac {a^4 x^4+24}{a^8}+c_2 e^{-a x}+c_4 e^{a x}+c_1 \cos (a x)+c_3 \sin (a x) \]