8.7.22 problem 38

Internal problem ID [828]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 38
Date solved : Monday, January 27, 2025 at 03:09:24 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: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.013 (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]
 

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