Internal problem ID [4699]
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 24.30.
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) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)+y(x)=sin(x),y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {5 \sin \relax (x )}{2}-\frac {x \cos \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 19
DSolve[{y''[x]+y[x]==Sin[x],{y[0]==0,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (5 \sin (x)-x \cos (x)) \\ \end{align*}