73.9.25 problem 14.3 (a)

Internal problem ID [15286]
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 : 14.3 (a)
Date solved : Tuesday, January 28, 2025 at 07:51:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 \,{\mathrm e}^{2 x} \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=9*exp(2*x),exp(3*x)],singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{x} c_{1} -9 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==9*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (-9 e^x+c_2 e^{2 x}+c_1\right ) \]