Internal problem ID [6440]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 4.
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 (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)+y(x)=sin(x),D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{1} -x \right ) \cos \left (x \right )}{2}+\frac {3 \sin \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[{y''[x]+y[x]==Sin[x],{y'[0] == 1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 \sin (x)}{2}+\left (-\frac {x}{2}+c_1\right ) \cos (x) \\ \end{align*}