Internal problem ID [10232]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+9*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{3 x}+c_{3} {\mathrm e}^{3 x} x \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 30
DSolve[y'''[x]-6*y''[x]+9*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} e^{3 x} (c_2 (3 x-1)+3 c_1)+c_3 \\ \end{align*}