Internal problem ID [14086]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 49.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-12 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)-diff(y(x),x)-12*y(x)=0,y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 \,{\mathrm e}^{7 x}+5\right ) {\mathrm e}^{-3 x}}{7} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 23
DSolve[{y''[x]-y'[x]-12*y[x]==0,{y[0]==1,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{7} e^{-3 x} \left (2 e^{7 x}+5\right ) \]