78.16.8 problem 8

Internal problem ID [18387]
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 : 8
Date solved : Tuesday, January 28, 2025 at 11:49:12 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }+y&=2 x^{3}-3 x^{2}+4 x +5 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 45

dsolve(diff(y(x),x$3)-2*diff(y(x),x)+y(x)=2*x^3-3*x^2+4*x+5,y(x), singsol=all)
 

\[ y = 2 x^{3}+9 x^{2}+40 x +73+{\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{\frac {\left (\sqrt {5}-1\right ) x}{2}}+c_3 \,{\mathrm e}^{-\frac {\left (\sqrt {5}+1\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 60

DSolve[D[y[x],{x,3}]-2*D[y[x],x]+y[x]==2*x^3-3*x^2+4*x+5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x^3+9 x^2+40 x+c_1 e^{-\frac {1}{2} \left (1+\sqrt {5}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {5}-1\right ) x}+c_3 e^x+73 \]