56.1.88 problem 87

Internal problem ID [8800]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 87
Date solved : Monday, January 27, 2025 at 05:02:46 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 26

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

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