Internal problem ID [14185]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}}=\cos \left (x \right ) \sin \left (x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(cos(y(x))/(1-sin(y(x)))^2*diff(y(x),x)=sin(x)^3*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\frac {\cos \left (2 x \right )^{2}+16 c_{1} -2 \cos \left (2 x \right )-15}{\cos \left (2 x \right )^{2}+16 c_{1} -2 \cos \left (2 x \right )+1}\right ) \]
✓ Solution by Mathematica
Time used: 28.843 (sec). Leaf size: 705
DSolve[Cos[y[x]]/(1-Sin[y[x]])^2*y'[x]==Sin[x]^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \arccos \left (-\frac {4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to 2 \arccos \left (-\frac {4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to -2 \arccos \left (\frac {-4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to 2 \arccos \left (\frac {-4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to -2 \arccos \left (-\frac {-4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to 2 \arccos \left (-\frac {-4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to -2 \arccos \left (\frac {4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to 2 \arccos \left (\frac {4+\sqrt {-4 \cos (2 x)+\cos (4 x)-13+c_1}}{\sqrt {2} \sqrt {8 \sin ^4(x)+c_1}}\right ) \\ y(x)\to -\frac {3 \pi }{2} \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ y(x)\to \frac {3 \pi }{2} \\ y(x)\to -2 \arccos \left (-\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}-4}{4 \sqrt {\sin ^4(x)}}\right ) \\ y(x)\to 2 \arccos \left (-\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}-4}{4 \sqrt {\sin ^4(x)}}\right ) \\ y(x)\to -2 \arccos \left (\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}-4}{4 \sqrt {\sin ^4(x)}}\right ) \\ y(x)\to 2 \arccos \left (\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}-4}{4 \sqrt {\sin ^4(x)}}\right ) \\ y(x)\to -2 \arccos \left (-\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}+4}{4 \sqrt {\sin ^4(x)}}\right ) \\ y(x)\to 2 \arccos \left (-\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}+4}{4 \sqrt {\sin ^4(x)}}\right ) \\ y(x)\to -2 \arccos \left (\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}+4}{4 \sqrt {\sin ^4(x)}}\right ) \\ y(x)\to 2 \arccos \left (\frac {\sqrt {-4 \cos (2 x)+\cos (4 x)-13}+4}{4 \sqrt {\sin ^4(x)}}\right ) \\ \end{align*}