64.11.9 problem 9

Internal problem ID [13459]
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
Date solved : Tuesday, January 28, 2025 at 05:44:31 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y&=-18 x^{2}+1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = {\mathrm e}^{-3 x} \left (\left (3 x^{2}+x +4\right ) {\mathrm e}^{3 x}+{\mathrm e}^{4 x} c_{1} +c_{3} {\mathrm e}^{x}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 35

DSolve[D[y[x],{x,3}]+4*D[y[x],{x,2}]+D[y[x],x]-6*y[x]==-18*x^2+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x^2+x+c_1 e^{-3 x}+c_2 e^{-2 x}+c_3 e^x+4 \]