36.1.19 problem 19

Internal problem ID [6274]
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
Date solved : Monday, January 27, 2025 at 01:52:44 PM
CAS classification : [_separable]

\begin{align*} \frac {y^{\prime }}{2}&=\sqrt {y+1}\, \cos \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.368 (sec). Leaf size: 11

dsolve([1/2*diff(y(x),x)=sqrt(1+y(x))*cos(x),y(Pi) = 0],y(x), singsol=all)
 

\[ y = \sin \left (x \right ) \left (\sin \left (x \right )+2\right ) \]

✓ Solution by Mathematica

Time used: 0.170 (sec). Leaf size: 23

DSolve[{1/2*D[y[x],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*}