Internal problem ID [6332]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {5 y^{\prime \prime }+2 y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \relax (x ) = \frac {25 \sqrt {19}\, {\mathrm e}^{-\frac {x}{5}} \sin \left (\frac {\sqrt {19}\, x}{5}\right )}{19} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 6
DSolve[{5*y''[x]+2*y'[x]+4*y[x]==0,{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ \end{align*}