Internal problem ID [6444]
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]]
\[ \boxed {y^{\prime \prime }+y-\sin \left (x \right )=0} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 0, y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([diff(y(x),x$2)+y(x)=sin(x),D(y)(1) = 0, y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (1-\tan \left (1\right )\right ) \sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.007 (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*}