7.9 problem 9

Internal problem ID [607]

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: 9.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

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

Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

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

\[ y \relax (x ) = \frac {\left ({\mathrm e}^{3 x}-1\right ) {\mathrm e}^{-2 x}}{3} \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 21

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

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