Internal problem ID [1982]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.3 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (\cos ^{2}\relax (x )+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve((cos(x)^2+y(x)*sin(2*x))*diff(y(x),x)+y(x)^2=0,y(x), singsol=all)
\[ c_{1}+\frac {y \relax (x )^{2} \sin \relax (x )}{\cos \relax (x )}+y \relax (x ) = 0 \]
✓ Solution by Mathematica
Time used: 1.873 (sec). Leaf size: 80
DSolve[(Cos[x]^2+y[x]*Sin[2*x])*y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \cot (x) \left (1+\sqrt {\sec ^2(x)} \sqrt {\cos (x) (\cos (x)+4 c_1 \sin (x))}\right ) \\ y(x)\to \frac {1}{2} \cot (x) \left (-1+\sqrt {\sec ^2(x)} \sqrt {\cos (x) (\cos (x)+4 c_1 \sin (x))}\right ) \\ y(x)\to 0 \\ \end{align*}