7.9.17 problem 39

Internal problem ID [265]
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 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 39
Date solved : Monday, January 27, 2025 at 02:43:08 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{\frac {x}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve([4*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=0,exp(x/2)],singsol=all)
 

\[ y = {\mathrm e}^{\frac {x}{2}} \left (c_2 x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

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

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