7.10 problem 10

Internal problem ID [608]

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: 10.
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 }+3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -1] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

dsolve([diff(y(x),x$2) +4*diff(y(x),x)+3*y(x) = 0,y(0) = 2, D(y)(0) = -1],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {5 \,{\mathrm e}^{-x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \]

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 23

DSolve[{y''[x]+4*y'[x]+3*y[x]==0,{y[0]==2,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} e^{-3 x} \left (5 e^{2 x}-1\right ) \\ \end{align*}