Internal problem ID [5203]
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]]
\[ \boxed {y^{\prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 6
dsolve([diff(y(x),x$2)-y(x)=0,y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 26
DSolve[{y''[x]-y[x]==Sin[x],{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-e^{-x}+5 e^x-2 \sin (x)\right ) \]