69.1.98 problem 145

Internal problem ID [14251]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 145
Date solved : Tuesday, January 28, 2025 at 06:23:19 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(x),x$4)-8*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 35

DSolve[D[y[x],{x,4}]-8*D[y[x],{x,2}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_3 e^{4 x}+x \left (c_4 e^{4 x}+c_2\right )+c_1\right ) \]