Internal problem ID [615]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {5}{4}}, y^{\prime }\relax (0) = -{\frac {3}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 13
dsolve([diff(y(x),x$2) -y(x) = 0,y(0) = 5/4, D(y)(0) = -3/4],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x}+\frac {{\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[x]-y[x]==0,{y[0]==5/4,y'[0]==-3/4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x}+\frac {e^x}{4} \\ \end{align*}