73.10.15 problem 15.6 (b)

Internal problem ID [15310]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.6 (b)
Date solved : Tuesday, January 28, 2025 at 07:52:10 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 16

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

\[ y = \frac {\left ({\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-3 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{4} e^{-3 x} \left (e^{4 x}-1\right ) \]