11.2.3 problem 10

Internal problem ID [1474]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 10
Date solved : Monday, January 27, 2025 at 04:57:46 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

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

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

\[ y = \left (c_4 x +c_3 \right ) {\mathrm e}^{2 x}+c_2 x +c_1 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 22

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

\[ y(x)\to x (x (c_4 x+c_3)+c_2)+c_1 \]