Internal problem ID [10919]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 18(k).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y-\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+cot(x)*diff(y(x),x)-csc(x)^2*y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\cot \left (x \right )+\csc \left (x \right )\right ) c_{2} +\frac {c_{1}}{\cot \left (x \right )+\csc \left (x \right )}-\frac {\cos \left (x \right )}{2}+\frac {\csc \left (x \right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 32
DSolve[y''[x]+Cot[x]*y'[x]-Csc[x]^2*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (-\cos (x)+x \csc (x)-2 i c_2 \cot (x)+2 c_1 \csc (x)) \\ \end{align*}