78.16.3 problem 3

Internal problem ID [18382]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 11:48:35 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=10 x^{3} {\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=10*x^3*exp(-2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (c_{2} +c_{1} x +\frac {1}{2} x^{5}\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==10*x^3*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-2 x} \left (x^5+2 c_2 x+2 c_1\right ) \]