62.22.3 problem Ex 3

Internal problem ID [12925]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:44:13 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

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

\[ y = \left (c_4 \,x^{2}+x c_3 +c_{2} \right ) {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

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

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