Internal problem ID [7241]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 521.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {3 x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right )+c_{2} {\mathrm e}^{-\frac {3 x}{2}} \cos \left (\frac {\sqrt {7}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 42
DSolve[y''[x]+3*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x/2} \left (c_2 \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {7} x}{2}\right )\right ) \\ \end{align*}