23.2.1 problem 4(a)

Internal problem ID [4118]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 4(a)
Date solved : Monday, January 27, 2025 at 08:36:41 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+15 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+8*diff(y(x),x)+15*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{-5 x}+{\mathrm e}^{-3 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+8*D[y[x],x]+15*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (c_2 e^{2 x}+c_1\right ) \]