Internal problem ID [4696]
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 24.28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y-{\mathrm e}^{x}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve([diff(y(x),x$2)-y(x)=exp(x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 \,{\mathrm e}^{-x}}{4}+\frac {\left (2 x +1\right ) {\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[{y''[x]-y[x]==Exp[x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} ((x-1) \sinh (x)+(x+2) \cosh (x)) \\ \end{align*}