9.1.2 problem problem 39

Internal problem ID [929]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear Equations. Page 288
Problem number : problem 39
Date solved : Monday, January 27, 2025 at 03:22:35 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: 0.002 (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: 0.013 (sec). Leaf size: 20

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

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