Internal problem ID [6381]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 88.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y^{\prime }\relax (0) = 0, y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve([diff(y(x),x$2)+diff(y(x),x)+y(x)=0,D(y)(0) = 0, y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\frac {x}{2}} \left (\sqrt {3}\, \sin \left (\frac {\sqrt {3}\, x}{2}\right )+3 \cos \left (\frac {\sqrt {3}\, x}{2}\right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 47
DSolve[{y''[x]+y'[x]+y[x]==0,{y'[0]==0,y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-x/2} \left (\sqrt {3} \sin \left (\frac {\sqrt {3} x}{2}\right )+3 \cos \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}