Internal problem ID [240]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 45.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-\left (\sin ^{4}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+9*y(x)=sin(x)^4,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}-\frac {\left (\cos ^{2}\left (2 x \right )\right )}{28}-\frac {\cos \left (2 x \right )}{10}+\frac {5}{84} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 39
DSolve[y''[x]+9*y[x]==Sin[x]^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{10} \cos (2 x)-\frac {1}{56} \cos (4 x)+c_1 \cos (3 x)+c_2 \sin (3 x)+\frac {1}{24} \\ \end{align*}