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 24.27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-\sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)-y(x)=sin(x),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {3 \,{\mathrm e}^{-x}}{4}+\frac {3 \,{\mathrm e}^{x}}{4}-\frac {\sin \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.015 (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*}