Internal problem ID [5204]
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]]
\[ \boxed {y^{\prime \prime }-y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.406 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)-y(x)=sin(x),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sin \left (x \right )}{2}+\frac {3 \sinh \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 26
DSolve[{y''[x]-y[x]==Sin[x],{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-e^{-x}+5 e^x-2 \sin (x)\right ) \]