38.4.2 problem 2

Internal problem ID [6488]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:07:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=54 x +18 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=54*x+18,y(x), singsol=all)
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{3 x}+6 x +6 \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==54*x+18,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{3 x}+x \left (6+c_2 e^{3 x}\right )+6 \]