Internal problem ID [6324]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF
VARIATION OF PARAMETERS. Page 71
Problem number: 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\cot \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+y(x)=cot(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -2-\cos \left (x \right ) \ln \left (\csc \left (x \right )-\cot \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 34
DSolve[y''[x]+y[x]==Cot[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sin (x)+\cos (x) \left (-\log \left (\sin \left (\frac {x}{2}\right )\right )+\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1\right )-2 \]