73.15.47 problem 22.11 (f)

Internal problem ID [15478]
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 : 22.11 (f)
Date solved : Tuesday, January 28, 2025 at 07:58:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=4*exp(3*x),y(x), singsol=all)
 

\[ y = \left (4 x +c_{2} \right ) {\mathrm e}^{3 x}+{\mathrm e}^{2 x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==4*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

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