78.16.25 problem 25 (a)

Internal problem ID [18404]
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 : 25 (a)
Date solved : Tuesday, January 28, 2025 at 11:49:30 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 24

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=exp(2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \left (\frac {1}{6} x^{3}+c_{1} +c_{2} x^{2}+c_3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{2 x} \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right ) \]