Internal problem ID [6449]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+y-\sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y^{\prime }\relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 80
dsolve([diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x),D(y)(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (c_{2} \sqrt {3}\, {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}}{2}\right )-c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}}{2}\right )+2 \sin \relax (1) {\mathrm e}^{-\frac {x}{2}+\frac {1}{2}}\right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\left (\sin \left (\frac {\sqrt {3}}{2}\right ) \sqrt {3}+\cos \left (\frac {\sqrt {3}}{2}\right )\right ) \left ({\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2}-\cos \relax (x )\right )}{\sin \left (\frac {\sqrt {3}}{2}\right ) \sqrt {3}+\cos \left (\frac {\sqrt {3}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.819 (sec). Leaf size: 4176
DSolve[{y'''[x]+y'[x]+y[x]==Sin[x],{y'[1] == 0}},y[x],x,IncludeSingularSolutions -> True]
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