73.17.33 problem 33

Internal problem ID [15567]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 08:02:15 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=576 x^{2} {\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)-9*diff(y(x),x)+14*y(x)=576*x^2*exp(-x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{7 x} c_{2} +{\mathrm e}^{2 x} c_{1} +\frac {\left (288 x^{2}+264 x +97\right ) {\mathrm e}^{-x}}{12} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 39

DSolve[D[y[x],{x,2}]-9*D[y[x],x]+14*y[x]==576*x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (24 x^2+22 x+c_1 e^{3 x}+c_2 e^{8 x}+\frac {97}{12}\right ) \]