62.22.4 problem Ex 4

Internal problem ID [12926]
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 4
Date solved : Tuesday, January 28, 2025 at 04:44:13 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+9*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \left (x c_3 +c_{2} \right ) {\mathrm e}^{3 x}+c_{1} \]

✓ Solution by Mathematica

Time used: 3.491 (sec). Leaf size: 89

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+9*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \int _1^xe^{3 K[1]} (c_1+c_2 K[1])dK[1]+c_3 \\ y(x)\to \frac {1}{3} c_1 e^{3 x}-\frac {e^3 c_1}{3}+c_3 \\ y(x)\to \frac {1}{9} c_2 e^{3 x} (3 x-1)-\frac {2 e^3 c_2}{9}+c_3 \\ \end{align*}