Internal problem ID [11815]
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: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+8 y=x^{3}+x +{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+8*y(x)=x^3+x+exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{4 x}}{2}+\frac {{\mathrm e}^{-2 x}}{24}+\frac {69}{256}+\frac {29 x}{64}+\frac {9 x^{2}}{32}+\frac {x^{3}}{8}+c_{2} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.699 (sec). Leaf size: 50
DSolve[y''[x]-6*y'[x]+8*y[x]==x^3+x+Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{256} \left (32 x^3+72 x^2+116 x+69\right )+\frac {e^{-2 x}}{24}+c_1 e^{2 x}+c_2 e^{4 x} \]