64.10.3 problem 3

Internal problem ID [13409]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 05:41:56 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(4*diff(y(x),x$2)-12*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {x}{2}}+c_{2} {\mathrm e}^{\frac {5 x}{2}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[4*D[y[x],{x,2}]-12*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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