Internal problem ID [2253]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y-\left (\cos ^{2}\relax (x )\right ) \left (\sin ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+6*y(x)=sin(x)^2*cos(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\sqrt {6}\, x \right ) c_{2}+\cos \left (\sqrt {6}\, x \right ) c_{1}+\frac {1}{48}+\frac {\cos \left (4 x \right )}{80} \]
✓ Solution by Mathematica
Time used: 0.352 (sec). Leaf size: 39
DSolve[y''[x]+6*y[x]==Sin[x]^2*Cos[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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} \\ \end{align*}