56.1.90 problem 88

Internal problem ID [8802]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 88
Date solved : Monday, January 27, 2025 at 05:02:51 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\\ y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.023 (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)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 47

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

\[ y(x)\to \frac {1}{3} e^{-x/2} \left (\sqrt {3} \sin \left (\frac {\sqrt {3} x}{2}\right )+3 \cos \left (\frac {\sqrt {3} x}{2}\right )\right ) \]