78.16.17 problem 17

Internal problem ID [18396]
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 : 17
Date solved : Tuesday, January 28, 2025 at 11:49:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)-7*diff(y(x),x)+12*y(x)=exp(2*x)*(x^3-5*x^2),y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{2} +c_{1} {\mathrm e}^{4 x}+\frac {\left (4 x^{3}-2 x^{2}-18 x -25\right ) {\mathrm e}^{2 x}}{8} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 45

DSolve[D[y[x],{x,2}]-7*D[y[x],x]+12*y[x]==Exp[2*x]*(x^3-5*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} e^{2 x} \left (4 x^3-2 x^2-18 x+8 c_1 e^x+8 c_2 e^{2 x}-25\right ) \]