71.10.1 problem 1

Internal problem ID [14496]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:42:39 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: 0.005 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.014 (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]
 

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