Internal problem ID [6449]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y-\sin \left (x \right )=0} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 0, y \left (2\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 156
dsolve([diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x),D(y)(1) = 0, y(2) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 \sin \left (1\right ) \left (\left (-\cos \left (\frac {\sqrt {3}}{2}\right )^{2}+\frac {1}{2}\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+\cos \left (\frac {\sqrt {3}\, x}{2}\right ) \cos \left (\frac {\sqrt {3}}{2}\right ) \sin \left (\frac {\sqrt {3}}{2}\right )\right ) {\mathrm e}^{-\frac {x}{2}+\frac {1}{2}}+\cos \left (2\right ) \left (\left (\sqrt {3}\, \sin \left (\frac {\sqrt {3}}{2}\right )+\cos \left (\frac {\sqrt {3}}{2}\right )\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+\cos \left (\frac {\sqrt {3}\, x}{2}\right ) \left (\sqrt {3}\, \cos \left (\frac {\sqrt {3}}{2}\right )-\sin \left (\frac {\sqrt {3}}{2}\right )\right )\right ) {\mathrm e}^{1-\frac {x}{2}}-\cos \left (x \right ) \left (\sqrt {3}\, \cos \left (\frac {\sqrt {3}}{2}\right )+\sin \left (\frac {\sqrt {3}}{2}\right )\right )}{\sqrt {3}\, \cos \left (\frac {\sqrt {3}}{2}\right )+\sin \left (\frac {\sqrt {3}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.841 (sec). Leaf size: 12765
DSolve[{y'''[x]+y'[x]+y[x]==Sin[x],{y'[1] == 0,y[2]==0}},y[x],x,IncludeSingularSolutions -> True]
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