Internal problem ID [249]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 54.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\left (\csc ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+y(x)=csc(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{2}+\cos \relax (x ) c_{1}-1-\ln \left (\frac {1-\cos \relax (x )}{\sin \relax (x )}\right ) \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 34
DSolve[y''[x]+y[x]==Csc[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sin (x)+\cos (x) \left (-\log \left (\sin \left (\frac {x}{2}\right )\right )+\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1\right )-1 \\ \end{align*}