Internal problem ID [8093]
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')]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2} \sin \relax (y)+2 x y^{\prime } \left (\cos ^{3}\relax (y)\right )-\sin \relax (y) \left (\cos ^{4}\relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 1.072 (sec). Leaf size: 1378
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)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 1.874 (sec). Leaf size: 134
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 -\text {ArcTan}\left (2 \sqrt {c_1} \sqrt {x+c_1}\right ) \\ y(x)\to \text {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 -\sec ^{-1}\left (-\sqrt {1-x^2}\right ) \\ y(x)\to \sec ^{-1}\left (-\sqrt {1-x^2}\right ) \\ y(x)\to \frac {x \tanh ^{-1}(x)}{\sqrt {-x^2}} \\ y(x)\to \sec ^{-1}\left (\sqrt {1-x^2}\right ) \\ \end{align*}