Internal problem ID [1998]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\sin \relax (x ) y^{\prime }+2 \cos \relax (x ) y-1=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 10
dsolve([sin(x)*diff(y(x),x)+2*y(x)*cos(x)=1,y(1/2*Pi) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\cos \relax (x )+1} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 14
DSolve[{Sin[x]*y'[x]+2*y[x]*Cos[x]==1,y[Pi/2]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {x}{2}\right ) \csc (x) \\ \end{align*}