Internal problem ID [11757]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+8 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+8*y(x)=0,y(0) = 1, D(y)(0) = 6],y(x), singsol=all)
\[ y \left (x \right ) = 2 \,{\mathrm e}^{4 x}-{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 20
DSolve[{y''[x]-6*y'[x]+8*y[x]==0,{y[0]==1,y'[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (2 e^{2 x}-1\right ) \]