Internal problem ID [2491]
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`]]
\[ \boxed {\left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve((cos(x)^2+y(x)*sin(2*x))*diff(y(x),x)+y(x)^2=0,y(x), singsol=all)
\[ c_{1} +y \left (x \right )^{2} \tan \left (x \right )+y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 23.536 (sec). Leaf size: 170
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 {\cot (x)}{2}-\frac {\csc (2 x) \sqrt {e^{-\text {arctanh}(\cos (2 x))} \left (4 c_1 \sin (2 x) e^{\text {arctanh}(\cos (2 x))}+\csc (2 x)+(\cos (2 x)+2) \cot (2 x)\right )}}{2 \sqrt {\csc (2 x) e^{-\text {arctanh}(\cos (2 x))}}} y(x)\to -\frac {\cot (x)}{2}+\frac {\csc (2 x) \sqrt {e^{-\text {arctanh}(\cos (2 x))} \left (4 c_1 \sin (2 x) e^{\text {arctanh}(\cos (2 x))}+\csc (2 x)+(\cos (2 x)+2) \cot (2 x)\right )}}{2 \sqrt {\csc (2 x) e^{-\text {arctanh}(\cos (2 x))}}} y(x)\to 0 \end{align*}