Internal problem ID [12338]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y \cot \left (x \right )=\csc \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve([diff(y(x),x)=cot(x)*y(x)+csc(x),y(1/2*Pi) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\cos \left (x \right )+\sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 12
DSolve[{y'[x]==Cot[x]*y[x]+Csc[x],{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x)-\cos (x) \]