Internal problem ID [618]
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: 22.
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 \relax (0) = 2, y^{\prime }\relax (0) = \beta ] \end {align*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 22
dsolve([4*diff(y(x),x$2) -y(x) = 0,y(0) = 2, D(y)(0) = beta],y(x), singsol=all)
\[ y \relax (x ) = \left (\beta +1\right ) {\mathrm e}^{\frac {x}{2}}-{\mathrm e}^{-\frac {x}{2}} \left (-1+\beta \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[{4*y''[x]-y[x]==0,{y[0]==2,y'[0]==\[Beta]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \left (\beta \sinh \left (\frac {x}{2}\right )+\cosh \left (\frac {x}{2}\right )\right ) \\ \end{align*}