78.16.2 problem 2

Internal problem ID [18381]
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 : 2
Date solved : Tuesday, January 28, 2025 at 11:48:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 31

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

\[ y = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} +\frac {\left (9 x^{2}-24 x +26\right ) {\mathrm e}^{2 x}}{27} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{27} e^{2 x} \left (9 x^2-24 x+26\right )+c_1 e^x+c_2 e^{-x} \]