Internal problem ID [8848]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 513.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {{y^{\prime }}^{2} \sin \left (y\right )+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4}=0} \]
✗ Solution by Maple
dsolve(diff(y(x),x)^2*sin(y(x))+2*x*diff(y(x),x)*cos(y(x))^3-sin(y(x))*cos(y(x))^4=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 1.829 (sec). Leaf size: 135
DSolve[-(Cos[y[x]]^4*Sin[y[x]]) + 2*x*Cos[y[x]]^3*y'[x] + Sin[y[x]]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arctan \left (2 \sqrt {c_1} \sqrt {x+c_1}\right ) \\ y(x)\to \arctan \left (2 \sqrt {c_1} \sqrt {x+c_1}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ y(x)\to -\arccos \left (-\frac {1}{\sqrt {1-x^2}}\right ) \\ y(x)\to \arccos \left (-\frac {1}{\sqrt {1-x^2}}\right ) \\ y(x)\to -\arccos \left (\frac {1}{\sqrt {1-x^2}}\right ) \\ y(x)\to \arccos \left (\frac {1}{\sqrt {1-x^2}}\right ) \\ \end{align*}