Internal problem ID [611]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant
Coefficients, page 144
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 y^{\prime }+3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 39
dsolve([diff(y(x),x$2) +5*diff(y(x),x)+3*y(x) = 0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (13+5 \sqrt {13}\right ) {\mathrm e}^{\frac {\left (-5+\sqrt {13}\right ) x}{2}}}{26}+\frac {\left (13-5 \sqrt {13}\right ) {\mathrm e}^{-\frac {\left (5+\sqrt {13}\right ) x}{2}}}{26} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 51
DSolve[{y''[x]+5*y'[x]+3*y[x]==0,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{26} e^{-\frac {1}{2} \left (5+\sqrt {13}\right ) x} \left (\left (13+5 \sqrt {13}\right ) e^{\sqrt {13} x}+13-5 \sqrt {13}\right ) \\ \end{align*}