Internal problem ID [11755]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-12 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)-diff(y(x),x)-12*y(x)=0,y(0) = 3, D(y)(0) = 5],y(x), singsol=all)
\[ y \left (x \right ) = \left (2 \,{\mathrm e}^{7 x}+1\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 18
DSolve[{y''[x]-y'[x]-12*y[x]==0,{y[0]==3,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x}+2 e^{4 x} \]