Internal problem ID [11730]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=2-12 x +6 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}+3 \,{\mathrm e}^{x}-2 x -\frac {4}{3} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 33
DSolve[y''[x]-5*y'[x]+6*y[x]==2-12*x+6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 x+3 e^x+c_1 e^{2 x}+c_2 e^{3 x}-\frac {4}{3} \]