Internal problem ID [5145]
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]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=54 x +18} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+6 x +6 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 27
DSolve[y''[x]-6*y'[x]+9*y[x]==54*x+18,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{3 x}+x \left (6+c_2 e^{3 x}\right )+6 \]