Internal problem ID [4360]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {2 x -y \sin \left (2 x \right )-\left (\sin ^{2}\relax (x )-2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 75
dsolve(2*x-y(x)*sin(2*x)=(sin(x)^2-2*y(x))*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{4}-\frac {\cos \left (2 x \right )}{4}-\frac {\sqrt {\cos ^{2}\left (2 x \right )-16 x^{2}-2 \cos \left (2 x \right )-16 c_{1}+1}}{4} \\ y \relax (x ) = \frac {1}{4}-\frac {\cos \left (2 x \right )}{4}+\frac {\sqrt {\cos ^{2}\left (2 x \right )-16 x^{2}-2 \cos \left (2 x \right )-16 c_{1}+1}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 87
DSolve[2*x-y[x]*Sin[2*x]==(Sin[x]^2-2*y[x])*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-\sqrt {-16 x^2+(\cos (2 x)-2) \cos (2 x)+1+16 c_1}-\cos (2 x)+1\right ) \\ y(x)\to \frac {1}{4} \left (\sqrt {-16 x^2+(\cos (2 x)-2) \cos (2 x)+1+16 c_1}-\cos (2 x)+1\right ) \\ \end{align*}