Internal problem ID [4940]
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]
\[ \boxed {y^{\prime }-\sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 21
dsolve([diff(y(x),x)=sqrt(1+sin(x))*(1+y(x)^2),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\sqrt {2}\, \left (\int _{0}^{x}\operatorname {csgn}\left (\sin \left (\frac {\pi }{4}+\frac {\textit {\_z1}}{2}\right )\right ) \sin \left (\frac {\pi }{4}+\frac {\textit {\_z1}}{2}\right )d \textit {\_z1} \right )+\frac {\pi }{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.305 (sec). Leaf size: 29
DSolve[{y'[x]==Sqrt[1+Sin[x]]*(1+y[x]^2),{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \tan \left (\frac {1}{4} \left (8 \sin \left (\frac {x}{2}\right )-8 \cos \left (\frac {x}{2}\right )+\pi +8\right )\right ) \]