Internal problem ID [10567]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, section 1.3. Exercises page 22
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+diff(y(x),x)-6*y(x)=0,y(0) = 6, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \left (4 \,{\mathrm e}^{5 x}+2\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[{y''[x]+y'[x]-6*y[x]==0,{y[0]==6,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (4 e^{5 x}+2\right ) \\ \end{align*}