78.16.16 problem 16

Internal problem ID [18395]
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 : 16
Date solved : Tuesday, January 28, 2025 at 11:49:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

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

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{x} c_{1} +{\mathrm e}^{2 x} \left (-x^{3}-6 x \right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 31

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

\[ y(x)\to e^x \left (-e^x x \left (x^2+6\right )+c_2 e^{2 x}+c_1\right ) \]