69.1.100 problem 147

Internal problem ID [14253]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 147
Date solved : Tuesday, January 28, 2025 at 06:23:20 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 30

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

\[ y = c_{1} {\mathrm e}^{a x}+c_{2} {\mathrm e}^{-a x}+c_{3} \sin \left (a x \right )+c_4 \cos \left (a x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 37

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

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