Internal problem ID [11588]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, section 1.3. Exercises page 22
Problem number: 3(a).
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 ) = 5, y^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)-diff(y(x),x)-12*y(x)=0,y(0) = 5, D(y)(0) = 6],y(x), singsol=all)
\[ y \left (x \right ) = \left (3 \,{\mathrm e}^{7 x}+2\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 20
DSolve[{y''[x]-y'[x]-12*y[x]==0,{y[0]==5,y'[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (3 e^{7 x}+2\right ) \]