Internal problem ID [6442]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 6.
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 \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 32
dsolve([diff(y(x),x$2)+y(x)=sin(x),y(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-2 c_{2} -1\right ) \tan \left (1\right )-x +1\right ) \cos \left (x \right )}{2}+\frac {\sin \left (x \right ) \left (1+2 c_{2} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 18
DSolve[{y''[x]+y[x]==Sin[x],{y[0] == 0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} x \cos (x)+c_2 \sin (x) \\ \end{align*}