Internal problem ID [11783]
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: 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y=-18 x^{2}+1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)+diff(y(x),x)-6*y(x)=-18*x^2+1,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-3 x} \left (\left (3 x^{2}+x +4\right ) {\mathrm e}^{3 x}+c_{1} {\mathrm e}^{4 x}+c_{3} {\mathrm e}^{x}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 35
DSolve[y'''[x]+4*y''[x]+y'[x]-6*y[x]==-18*x^2+1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x^2+x+c_1 e^{-3 x}+c_2 e^{-2 x}+c_3 e^x+4 \]