Internal problem ID [11787]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=10*exp(2*x)-18*exp(3*x)-6*x-11,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-3 x} \left (\left (2 x +c_{1} -\frac {2}{5}\right ) {\mathrm e}^{5 x}+\left (x +2\right ) {\mathrm e}^{3 x}+c_{2} -3 \,{\mathrm e}^{6 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.299 (sec). Leaf size: 38
DSolve[y''[x]+y'[x]-6*y[x]==10*Exp[2*x]-18*Exp[3*x]-6*x-11,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x-3 e^{3 x}+c_1 e^{-3 x}+e^{2 x} \left (2 x-\frac {2}{5}+c_2\right )+2 \]