Internal problem ID [4374]
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: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } \left (\sin ^{2}\relax (x )\right )+\sin ^{2}\relax (x )+\left (x +y\right ) \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 19
dsolve(sin(x)^2*diff(y(x),x)+(sin(x)^2+(x+y(x))*sin(2*x))=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 c_{1}}{-1+\cos \left (2 x \right )}-x \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 16
DSolve[Sin[x]^2*y'[x]+(Sin[x]^2+(x+y[x])*Sin[2*x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+c_1 \csc ^2(x) \\ \end{align*}