7.3.28 problem 28

Internal problem ID [68]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 28
Date solved : Friday, February 07, 2025 at 07:47:42 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (4\right )&=\frac {\pi }{4} \end{align*}

✓ Solution by Maple

Time used: 0.115 (sec). Leaf size: 10

dsolve([2*sqrt(x)*diff(y(x),x)= cos(y(x))^2,y(4) = 1/4*Pi],y(x), singsol=all)
 

\[ y = \arctan \left (\sqrt {x}-1\right ) \]

✓ Solution by Mathematica

Time used: 0.459 (sec). Leaf size: 17

DSolve[{2*Sqrt[x]*D[y[x],x]== Cos[y[x]]^2,{y[4]==Pi/4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\arctan \left (1-\sqrt {x}\right ) \]