Internal problem ID [162]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 6.
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=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 7, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+diff(y(x),x)-6*y(x)=0,y(0) = 7, D(y)(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = \left (4 \,{\mathrm e}^{5 x}+3\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[{y''[x]+y'[x]-6*y[x]==0,{y[0]==7,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (4 e^{5 x}+3\right ) \\ \end{align*}