7.8.25 problem 38

Internal problem ID [239]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 38
Date solved : Monday, January 27, 2025 at 02:42:52 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(4*diff(y(x),x$2)+8*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{-\frac {x}{2}}+c_2 \,{\mathrm e}^{-\frac {3 x}{2}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

DSolve[4*D[y[x],{x,2}]+8*D[y[x],x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x/2} \left (c_2 e^x+c_1\right ) \]