Internal problem ID [12434]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)-y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x}}{2}-\frac {{\mathrm e}^{-x}}{2} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 21
DSolve[{y''[x]-y[x]==0,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-x} \left (e^{2 x}-1\right ) \]