10.7.12 problem 12

Internal problem ID [1260]
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 : 12
Date solved : Monday, January 27, 2025 at 04:48:10 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

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

\[ y = -1-{\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 14

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

\[ y(x)\to -e^{-3 x}-1 \]