Internal problem ID [6443]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 6.
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 (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.06 (sec). Leaf size: 37
dsolve([diff(y(x),x$2)+y(x)=sin(x),y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\left (1-x \right ) \cos \relax (x )+\left (2 c_{2}+1\right ) \sin \relax (x )\right ) \cos \relax (1)-2 \left (c_{2}+\frac {1}{2}\right ) \sin \relax (1) \cos \relax (x )}{2 \cos \relax (1)} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 18
DSolve[{y''[x]+y[x]==Sin[x],{y[0] == 0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} x \cos (x)+c_2 \sin (x) \\ \end{align*}