Internal problem ID [632]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+ 4*diff(y(x),x)+625/100*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-2 x} \sin \left (\frac {3 x}{2}\right )+c_{2} {\mathrm e}^{-2 x} \cos \left (\frac {3 x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[y''[x]+4*y'[x]+625/100*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (c_2 \cos \left (\frac {3 x}{2}\right )+c_1 \sin \left (\frac {3 x}{2}\right )\right ) \\ \end{align*}