Internal problem ID [11821]
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: 47.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y={\mathrm e}^{2 x} x +{\mathrm e}^{3 x} x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=x*exp(2*x)+x^2*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{4}+24 c_{3} x^{2}+24 c_{2} x +24 c_{1} \right ) {\mathrm e}^{2 x}}{24}+{\mathrm e}^{3 x} \left (x^{2}-6 x +12\right ) \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 47
DSolve[y'''[x]-6*y''[x]+12*y'[x]-8*y[x]==x*Exp[2*x]+x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^{2 x} \left (x^4+24 e^x \left (x^2-6 x+12\right )+24 c_3 x^2+24 c_2 x+24 c_1\right ) \]