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]]
\[ \boxed {4 y^{\prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = \beta ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \left (1+\beta \right ) {\mathrm e}^{\frac {x}{2}}-\left (\beta -1\right ) {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 25
DSolve[{4*y''[x]-y[x]==0,{y[0]==2,y'[0]==\[Beta]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (-\beta +(\beta +1) e^x+1\right ) \]