56.1.41 problem 41

Internal problem ID [8753]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 41
Date solved : Monday, January 27, 2025 at 04:46:42 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime }+2 y^{\prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 20

dsolve([5*diff(y(x),x$2)+2*diff(y(x),x)+4*y(x)=0,y(0) = 0, D(y)(0) = 5],y(x), singsol=all)
 

\[ y = \frac {25 \sqrt {19}\, {\mathrm e}^{-\frac {x}{5}} \sin \left (\frac {\sqrt {19}\, x}{5}\right )}{19} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 6

DSolve[{5*D[y[x],{x,2}]+2*D[y[x],x]+4*y[x]==0,{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 0 \]