Internal problem ID [4382]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-6 y-6=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)+diff(y(x),x)-6*y(x)=6,y(0) = 1, D(y)(0) = 4],y(x), singsol=all)
\[ y \relax (x ) = 2 \,{\mathrm e}^{2 x}-1 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 14
DSolve[{y''[x]+y'[x]-6*y[x]==6,{y[0]==1,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^{2 x}-1 \\ \end{align*}