Internal problem ID [7199]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 0, y \left (2\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 33
dsolve([diff(y(x),x$2)+y(x)=sin(x),D(y)(1) = 0, y(2) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-x +\cos \left (2\right )-\sin \left (2\right )+1\right ) \cos \left (x \right )}{2}+\frac {\sin \left (x \right ) \left (\sin \left (2\right )-\tan \left (1\right )+\cos \left (2\right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 39
DSolve[{y''[x]+y[x]==Sin[x],{y'[1] == 0,y[2]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} (\sec (1) \sin (x) (-\sin (1)+\sin (3)+\cos (1)+\cos (3))-2 \cos (x) (x-1+\sin (2)-\cos (2))) \]