Internal problem ID [894]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } x +\left (1+x \cot \left (x \right )\right ) y=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve([x*diff(y(x),x) + (1+x*cot(x))*y(x)=0,y(1/2*Pi) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\csc \left (x \right ) \pi }{x} \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 66
DSolve[{y'[x] +(1+x*Cot[x])*y[x]==0,y[Pi/2]==2},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2^{1+\frac {\pi }{2}} \left (1-e^{2 i x}\right )^{-x} \exp \left (-\frac {1}{12} i \left (-6 \operatorname {PolyLog}\left (2,e^{2 i x}\right )-6 x (x+2 i)+\pi ^2+6 i \pi \right )\right ) \]