Internal problem ID [6441]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)+y(x)=sin(x),D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-x +2 c_{1}\right ) \cos \relax (x )}{2}+\frac {3 \sin \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.011 (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*}