Internal problem ID [12284]
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(i).
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 ) = 2, y^{\prime }\left (0\right ) = -5] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(0) = 2, D(y)(0) = -5],y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{2 x}+3 \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 19
DSolve[{y''[x]-y'[x]-2*y[x]==0,{y[0]==2,y'[0]==-5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{-x} \left (e^{3 x}-3\right ) \]