Internal problem ID [12267]
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime } \cot \left (x \right )-\csc \left (x \right )^{2} y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+cot(x)*diff(y(x),x)-csc(x)^2*y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = -\cos \left (\frac {x}{2}\right )^{2}+\frac {1}{2}+\frac {\sec \left (\frac {x}{2}\right ) \csc \left (\frac {x}{2}\right ) x}{4}+\cot \left (\frac {x}{2}\right ) c_{2} +\tan \left (\frac {x}{2}\right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.349 (sec). Leaf size: 45
DSolve[y''[x]+Cot[x]*y'[x]-Csc[x]^2*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x \csc (x)+\frac {2 c_1}{\sqrt {\sin ^2(x)}}+\cos (x) \left (-1-\frac {2 i c_2}{\sqrt {\sin ^2(x)}}\right )\right ) \]