10.9.3 problem 3

Internal problem ID [1305]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 3
Date solved : Monday, January 27, 2025 at 04:50:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-4 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)-4*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: 0.012 (sec). Leaf size: 24

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

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