12.8.7 problem 10

Internal problem ID [1743]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:34:06 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y = c_1 \,{\mathrm e}^{3 x}+c_2 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

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

\[ y(x)\to e^{-x} \left (c_2 e^{4 x}+c_1\right ) \]