Internal problem ID [53]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 \sqrt {x}\, y^{\prime }-\left (\cos ^{2}\relax (y)\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (4) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.108 (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)
\[ y \relax (x ) = \arctan \left (-1+\sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.459 (sec). Leaf size: 17
DSolve[{2*x^(1/2)*y'[x] == Cos[y[x]]^2,y[4]==Pi/4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcTan}\left (1-\sqrt {x}\right ) \\ \end{align*}