Internal problem ID [6334]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 43.
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 }+4 y-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+diff(y(x),x)+4*y(x)=sin(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right ) c_{2}+{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right ) c_{1}-\frac {\cos \relax (x )}{10}+\frac {3 \sin \relax (x )}{10} \]
✓ Solution by Mathematica
Time used: 0.564 (sec). Leaf size: 55
DSolve[y''[x]+y'[x]+4*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 \sin (x)}{10}-\frac {\cos (x)}{10}+e^{-x/2} \left (c_2 \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {15} x}{2}\right )\right ) \\ \end{align*}