35.8.19 problem 19

Internal problem ID [6226]
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
Date solved : Monday, January 27, 2025 at 01:48:48 PM
CAS classification : [_linear]

\begin{align*} \sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right )&=0 \end{align*}

✓ 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)
 

\[ y = -\frac {2 c_{1}}{-1+\cos \left (2 x \right )}-x \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 27

DSolve[Sin[x]^2*D[y[x],x]+(Sin[x]^2+(x+y[x])*Sin[2*x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \csc ^2(x) (-x+x \cos (2 x)+2 c_1) \]