Internal problem ID [4695]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page
248
Problem number: Problem 24.26.
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*} [y \relax (0) = 1, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 6
dsolve([diff(y(x),x$2)-y(x)=0,y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 20
DSolve[{y''[x]-y[x]==Sin[x],{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sin (x)}{2}+\frac {3 \sinh (x)}{2}+\cosh (x) \\ \end{align*}