82.26.2 problem Ex. 2

Internal problem ID [18874]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 67
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:33:13 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-m^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

dsolve(diff(y(x),x$4)-m^2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 53

DSolve[D[y[x],{x,4}]-m^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 e^{-\sqrt {m} x}+c_4 e^{\sqrt {m} x}+c_1 \cos \left (\sqrt {m} x\right )+c_3 \sin \left (\sqrt {m} x\right ) \]