73.9.12 problem 14.2 (b)

Internal problem ID [15273]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.2 (b)
Date solved : Tuesday, January 28, 2025 at 07:51:26 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=0,exp(5*x)],singsol=all)
 

\[ y = {\mathrm e}^{5 x} \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{5 x} (c_2 x+c_1) \]