Internal problem ID [12287]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises 1.3, page 27
Problem number: 8 b(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 (0\right ) = 0, y^{\prime }\left (2\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(0) = 0, D(y)(2) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{2-x} \left ({\mathrm e}^{3 x}-1\right )}{2 \,{\mathrm e}^{6}+1} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 29
DSolve[{y''[x]-y'[x]-2*y[x]==0,{y[0]==0,y'[2]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{2-x} \left (e^{3 x}-1\right )}{1+2 e^6} \]