8.3.27 problem 28

Internal problem ID [703]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 28
Date solved : Monday, January 27, 2025 at 02:58:31 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: 0.041 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.437 (sec). Leaf size: 17

DSolve[{2*x^(1/2)*D[y[x],x] == Cos[y[x]]^2,y[4]==Pi/4},y[x],x,IncludeSingularSolutions -> True]
 

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