73.15.21 problem 22.7 (f)

Internal problem ID [15452]
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 : 22.7 (f)
Date solved : Tuesday, January 28, 2025 at 07:56:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=(12*x-4)*exp(-5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-5 x} \left (\left (c_{1} x +c_{2} \right ) {\mathrm e}^{6 x}+\frac {x}{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==(12*x-4)*Exp[-5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-5 x} x+e^x (c_2 x+c_1) \]