62.21.4 problem Ex 4

Internal problem ID [12922]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 43. Page 92
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:44:11 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{2 x} c_{2} +c_3 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

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

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