Internal problem ID [6445]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 8.
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, y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 24
dsolve([diff(y(x),x$2)+y(x)=sin(x),D(y)(1) = 0, y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\sin \relax (x ) \sin \relax (1)}{2 \cos \relax (1)}+\frac {\sin \relax (x )}{2}-\frac {x \cos \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 23
DSolve[{y''[x]+y[x]==Sin[x],{y'[1] == 0,y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (\sin (x)-x \cos (x)-\tan (1) \sin (x)) \\ \end{align*}