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]
\[ \boxed {2 \sqrt {x}\, y^{\prime }-\cos \left (y\right )^{2}=0} \] With initial conditions \begin {align*} \left [y \left (4\right ) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.109 (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)
\[ y \left (x \right ) = \arctan \left (-1+\sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.46 (sec). Leaf size: 17
DSolve[{2*x^(1/2)*y'[x] == Cos[y[x]]^2,y[4]==Pi/4},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\arctan \left (1-\sqrt {x}\right ) \]