35.6.2 problem 2

Internal problem ID [6152]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:38:31 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=16 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=16,y(x), singsol=all)
 

\[ y = 4+\left (c_1 x +c_2 \right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==16,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 4+e^{2 x} (c_2 x+c_1) \]