Internal problem ID [7197]
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]]
\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 27
dsolve([diff(y(x),x$2)+y(x)=sin(x),D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 \cot \left (1\right ) c_{2} -x +1\right ) \cos \left (x \right )}{2}+\frac {\sin \left (x \right ) \left (2 c_{2} +1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 35
DSolve[{y''[x]+y[x]==Sin[x],{y'[1] == 0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} ((1-\tan (1)+2 c_1 \tan (1)) \sin (x)-(x-2 c_1) \cos (x)) \]