Internal problem ID [13242]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.2 (c).
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 ) = 8, y^{\prime }\left (0\right ) = -9] \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) = 8, D(y)(0) = -9],y(x), singsol=all)
\[ y = \left (3 \,{\mathrm e}^{5 x}+5\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 20
DSolve[{y''[x]+y'[x]-6*y[x]==0,{y[0]==8,y'[0]==-9}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (3 e^{5 x}+5\right ) \]