Internal problem ID [4637]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y-54 x -18=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=54*x+18,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{3 x} c_{1} x +6 x +6 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[y''[x]-6*y'[x]+9*y[x]==54*x+18,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 6 (x+1)+e^{3 x} (c_2 x+c_1) \\ \end{align*}