7.10.12 problem 12

Internal problem ID [282]
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 : 12
Date solved : Monday, January 27, 2025 at 02:43:19 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 32

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

\[ y(x)\to e^x \left (c_3 \left (x^2-2 x+2\right )+c_2 (x-1)+c_1\right )+c_4 \]