7.10.11 problem 11

Internal problem ID [281]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:43:19 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x$4)-8*diff(y(x),x$3)+16*diff(y(x),x$2)=0,y(x), singsol=all)
 

\[ y = \left (c_4 x +c_3 \right ) {\mathrm e}^{4 x}+c_2 x +c_1 \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 34

DSolve[D[y[x],{x,4}]-8*D[y[x],{x,3}]+16*D[y[x],{x,2}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{32} e^{4 x} (c_2 (2 x-1)+2 c_1)+c_4 x+c_3 \]