78.16.9 problem 9

Internal problem ID [18388]
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 : 9
Date solved : Tuesday, January 28, 2025 at 11:49:12 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

\[ y = \sin \left (\frac {x}{2}\right ) c_{2} +\cos \left (\frac {x}{2}\right ) c_{1} +x^{4}-48 x^{2}+384 \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 33

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

\[ y(x)\to x^4-48 x^2+c_1 \cos \left (\frac {x}{2}\right )+c_2 \sin \left (\frac {x}{2}\right )+384 \]