9.2.2 problem problem 11

Internal problem ID [936]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 11
Date solved : Monday, January 27, 2025 at 03:22:36 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: 0.001 (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: 0.035 (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]
 

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