73.15.29 problem 22.10 (b)

Internal problem ID [15460]
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 : 22.10 (b)
Date solved : Tuesday, January 28, 2025 at 07:56:41 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=4 x \,{\mathrm e}^{6 x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=4*x*exp(6*x),y(x), singsol=all)
 

\[ y = \frac {\left (8 \,{\mathrm e}^{8 x} x -9 \,{\mathrm e}^{8 x}+16 \,{\mathrm e}^{7 x} c_{2} +16 c_{1} \right ) {\mathrm e}^{-2 x}}{16} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==4*x*Exp[6*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} e^{6 x} (8 x-9)+c_1 e^{-2 x}+c_2 e^{5 x} \]