Internal problem ID [11793]
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: 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 42
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=x*exp(x)-4*exp(2*x)+6*exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (4 x +c_{2} \right ) {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{3 x}+{\mathrm e}^{4 x}+\frac {\left (2 x^{2}+8 c_{1} +6 x +7\right ) {\mathrm e}^{x}}{8} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 53
DSolve[y'''[x]-6*y''[x]+11*y'[x]-6*y[x]==x*Exp[x]-4*Exp[2*x]+6*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} e^x \left (2 x^2+6 x+8 e^{3 x}+8 e^x (4 x+c_2)+8 c_3 e^{2 x}+7+8 c_1\right ) \]