56.1.89 problem 88

Internal problem ID [8801]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 88
Date solved : Monday, January 27, 2025 at 05:02:49 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 29

dsolve([diff(y(x),x$2)+diff(y(x),x)+y(x)=0,D(y)(0) = 0],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{2}} c_{1} \left (\sqrt {3}\, \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\sin \left (\frac {\sqrt {3}\, x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 44

DSolve[{D[y[x],{x,2}]+D[y[x],x]+y[x]==0,{Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-x/2} \left (\sin \left (\frac {\sqrt {3} x}{2}\right )+\sqrt {3} \cos \left (\frac {\sqrt {3} x}{2}\right )\right ) \]