78.16.12 problem 12

Internal problem ID [18391]
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 : 12
Date solved : Tuesday, January 28, 2025 at 11:49:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 44

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

\[ y = c_{2} {\mathrm e}^{\frac {\left (\sqrt {5}-1\right ) x}{2}}+{\mathrm e}^{-\frac {\left (\sqrt {5}+1\right ) x}{2}} c_{1} +x^{4}+4 x^{3}+24 x^{2}+69 x +117 \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 57

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

\[ y(x)\to x^4+4 x^3+24 x^2+69 x+c_1 e^{-\frac {1}{2} \left (1+\sqrt {5}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {5}-1\right ) x}+117 \]