69.1.93 problem 140

Internal problem ID [14246]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 140
Date solved : Tuesday, January 28, 2025 at 06:23:17 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-5*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{4 x}+c_4 \,{\mathrm e}^{3 x}+{\mathrm e}^{x} c_{1} +c_{3} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 35

DSolve[D[y[x],{x,4}]-5*D[y[x],{x,2}]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_2 e^x+e^{3 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]