Internal problem ID [4422]
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: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {y^{\prime }}{2}-\sqrt {y+1}\, \cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \left (\pi \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.324 (sec). Leaf size: 11
dsolve([1/2*diff(y(x),x)=sqrt(1+y(x))*cos(x),y(Pi) = 0],y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) \left (\sin \relax (x )+2\right ) \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 23
DSolve[{1/2*y'[x]==Sqrt[1+y[x]]*Cos[x],{y[Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (\sin (x)-2) \sin (x) \\ y(x)\to \sin (x) (\sin (x)+2) \\ \end{align*}