69.1.96 problem 143

Internal problem ID [14249]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 143
Date solved : Tuesday, January 28, 2025 at 06:23:19 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x$5)-4*diff(y(x),x$3)=0,y(x), singsol=all)
 

\[ y = c_{1} +c_{2} x +c_{3} x^{2}+c_4 \,{\mathrm e}^{2 x}+c_5 \,{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 39

DSolve[D[y[x],{x,5}]-4*D[y[x],{x,3}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} c_1 e^{2 x}-\frac {1}{8} c_2 e^{-2 x}+x (c_5 x+c_4)+c_3 \]