Internal problem ID [614]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant
Coefficients, page 144
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }-y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-2\right ) = 1, y^{\prime }\left (-2\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 21
dsolve([4*diff(y(x),x$2) -y(x) = 0,y(-2) = 1, D(y)(-2) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \,{\mathrm e}^{-1-\frac {x}{2}}}{2}-\frac {{\mathrm e}^{1+\frac {x}{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[{4*y''[x]-y[x]==0,{y[-2]==1,y'[-2]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cosh \left (\frac {x+2}{2}\right )-2 \sinh \left (\frac {x+2}{2}\right ) \\ \end{align*}