76.13.35 problem 35

Internal problem ID [17617]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 10:45:35 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: 0.016 (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: 0.015 (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]
 

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