15.9.3 problem 17

Internal problem ID [3060]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 17
Date solved : Monday, January 27, 2025 at 07:18:56 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+7*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-3 x}+c_2 \,{\mathrm e}^{-4 x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+7*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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