18.1.22 problem Problem 14.26

Internal problem ID [3478]
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
Date solved : Monday, January 27, 2025 at 07:38:30 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } \sin \left (x \right )+2 y \cos \left (x \right )&=1 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.015 (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)
 

\[ y \left (x \right ) = \frac {1}{\cos \left (x \right )+1} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 14

DSolve[{Sin[x]*D[y[x],x]+2*y[x]*Cos[x]==1,y[Pi/2]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \tan \left (\frac {x}{2}\right ) \csc (x) \]