19.1.14 problem 14

Internal problem ID [3528]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 14
Date solved : Monday, January 27, 2025 at 07:40:40 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: 0.372 (sec). Leaf size: 15

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)
 

\[ y \left (x \right ) = \frac {\pi }{2}-\arcsin \left (\frac {\sec \left (x \right )}{2}\right ) \]

✓ Solution by Mathematica

Time used: 5.987 (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]
 

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