73.15.27 problem 22.9 (e)

Internal problem ID [15458]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.9 (e)
Date solved : Tuesday, January 28, 2025 at 07:56:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=10 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=10*exp(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} \left (c_{1} x +5 x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==10*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (5 x^2+c_2 x+c_1\right ) \]