Internal problem ID [190]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.2, second order linear equations. Page 311
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-3 y-6=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = 11] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 16
dsolve([diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=6,y(0) = 3, D(y)(0) = 11],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x}+4 \,{\mathrm e}^{3 x}-2 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 19
DSolve[{y''[x]-2*y'[x]-3*y[x]==6,{y[0]==3,y'[0]==11}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x}+4 e^{3 x}-2 \\ \end{align*}