20.7.18 problem Problem 47

Internal problem ID [3733]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 47
Date solved : Monday, January 27, 2025 at 07:56:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y&=\sin \left (x \right )^{2} \cos \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)+6*y(x)=sin(x)^2*cos(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \sin \left (x \sqrt {6}\right ) c_{2} +\cos \left (x \sqrt {6}\right ) c_{1} +\frac {1}{48}+\frac {\cos \left (4 x \right )}{80} \]

✓ Solution by Mathematica

Time used: 0.753 (sec). Leaf size: 39

DSolve[D[y[x],{x,2}]+6*y[x]==Sin[x]^2*Cos[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{80} \cos (4 x)+c_1 \cos \left (\sqrt {6} x\right )+c_2 \sin \left (\sqrt {6} x\right )+\frac {1}{48} \]