Internal problem ID [10239]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 47. Particular
integral. Page 100
Problem number: Ex 1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }-{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(diff(y(x),x$3)-diff(y(x),x$2)-2*diff(y(x),x)=exp(-x),y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-x}+\frac {c_{2} {\mathrm e}^{2 x}}{2}+\frac {x \,{\mathrm e}^{-x}}{3}+\frac {{\mathrm e}^{-x}}{3}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 37
DSolve[y'''[x]-y''[x]-2*y'[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} e^{-x} (3 x+4-9 c_1)+\frac {1}{2} c_2 e^{2 x}+c_3 \\ \end{align*}