Internal problem ID [6444]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 7.
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^{\prime }\relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.098 (sec). Leaf size: 31
dsolve([diff(y(x),x$2)+y(x)=sin(x),D(y)(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) \left (\frac {1}{2}+\frac {\cos \relax (1) c_{2}}{\sin \relax (1)}\right )+\frac {\sin \relax (x )}{2}-\frac {x \cos \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 33
DSolve[{y''[x]+y[x]==Sin[x],{y'[1] == 0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (\sin (x)-((x-2 c_1) \cos (x))+(-1+2 c_1) \tan (1) \sin (x)) \\ \end{align*}