Internal problem ID [2635]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\frac {\sin \left (y+x \right )}{\sin \left (y\right ) \cos \left (x \right )}=1} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.172 (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)
\[ y \left (x \right ) = \frac {\pi }{2}-\arcsin \left (\frac {\sec \left (x \right )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 6.259 (sec). Leaf size: 12
DSolve[{y'[x]==1-(Sin[x+y[x]])/(Sin[y[x]]*Cos[x]),{y[Pi/4]==Pi/4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arccos \left (\frac {\sec (x)}{2}\right ) \]