Internal problem ID [11818]
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: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y={\mathrm e}^{x} x^{4}+x^{3} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=x^4*exp(x)+x^3*exp(2*x)+x^2*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{3}+6 x^{2}+18 x +24\right ) {\mathrm e}^{2 x}+\frac {\left (x^{4}+12 c_{1} x +12 c_{2} \right ) {\mathrm e}^{3 x}}{12}+\frac {\left (x^{4}+4 x^{3}+9 x^{2}+12 x +\frac {15}{2}\right ) {\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 1.391 (sec). Leaf size: 70
DSolve[y''[x]-6*y'[x]+9*y[x]==x^4*Exp[x]+x^3*Exp[2*x]+x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (\frac {x^4}{4}+e^{2 x} \left (\frac {x^4}{12}+c_2 x+c_1\right )+x^3+\frac {9 x^2}{4}+e^x \left (x^3+6 x^2+18 x+24\right )+3 x+\frac {15}{8}\right ) \]