20.2.14 problem Problem 14

Internal problem ID [3606]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations. page 43
Problem number : Problem 14
Date solved : Monday, January 27, 2025 at 07:47:25 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=\frac {\pi }{4} \end{align*}

✓ Solution by Maple

Time used: 2.569 (sec). Leaf size: 9

dsolve([diff(y(x),x)=1-(sin(x+y(x)))/(sin(y(x))*cos(x)),y(1/4*Pi) = 1/4*Pi],y(x), singsol=all)
 

\[ y \left (x \right ) = \arccos \left (\frac {\sec \left (x \right )}{2}\right ) \]

✓ Solution by Mathematica

Time used: 5.941 (sec). Leaf size: 12

DSolve[{D[y[x],x]==1-(Sin[x+y[x]])/(Sin[y[x]]*Cos[x]),{y[Pi/4]==Pi/4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arccos \left (\frac {\sec (x)}{2}\right ) \]