Internal problem ID [12605]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises 1.3, page 27
Problem number: 8 a(ii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 3, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(1) = 3, D(y)(1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {7 \,{\mathrm e}^{1-x}}{3}+\frac {2 \,{\mathrm e}^{2 x -2}}{3} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 28
DSolve[{y''[x]-y'[x]-2*y[x]==0,{y[1]==3,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {7 e^{1-x}}{3}+\frac {2}{3} e^{2 x-2} \]