Internal problem ID [4432]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 27 part(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {1+\sin \relax (x )}\, \left (1+y^{2}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.123 (sec). Leaf size: 21
dsolve([diff(y(x),x)=sqrt(1+sin(x))*(1+y(x)^2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (\int _{0}^{x}\sqrt {\sin \left (\textit {\_z1} \right )+1}d \textit {\_z1} +\frac {\pi }{4}\right )}{\cos \left (\int _{0}^{x}\sqrt {\sin \left (\textit {\_z1} \right )+1}d \textit {\_z1} +\frac {\pi }{4}\right )} \]
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 29
DSolve[{y'[x]==Sqrt[1+Sin[x]]*(1+y[x]^2),{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {1}{4} \left (8 \sin \left (\frac {x}{2}\right )-8 \cos \left (\frac {x}{2}\right )+\pi +8\right )\right ) \\ \end{align*}