64.9.8 problem 9

Internal problem ID [13406]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 124
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:41:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2-12 x +6 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=2-12*x+6*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{2 x} c_{1} +3 \,{\mathrm e}^{x}-2 x -\frac {4}{3} \]

✓ Solution by Mathematica

Time used: 0.241 (sec). Leaf size: 78

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==2-12*x+6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\int _1^x-2 e^{-2 K[1]} \left (-6 K[1]+3 e^{K[1]}+1\right )dK[1]+e^x \int _1^x2 e^{-3 K[2]} \left (-6 K[2]+3 e^{K[2]}+1\right )dK[2]+c_2 e^x+c_1\right ) \]