Internal problem ID [8687]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 351.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 55
dsolve(diff(y(x),x)*cos(y(x))+x*sin(y(x))*cos(y(x))^2-sin(y(x))^3 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \arcsin \left (\frac {1}{\sqrt {1-\sqrt {\pi }\, \operatorname {erf}\left (x \right ) {\mathrm e}^{x^{2}}-2 c_{1} {\mathrm e}^{x^{2}}}}\right ) \\ y \left (x \right ) &= -\arcsin \left (\frac {1}{\sqrt {1-\sqrt {\pi }\, \operatorname {erf}\left (x \right ) {\mathrm e}^{x^{2}}-2 c_{1} {\mathrm e}^{x^{2}}}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.366 (sec). Leaf size: 61
DSolve[x*Cos[y[x]]^2*Sin[y[x]] - Sin[y[x]]^3 + Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right ) \\ y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right ) \\ \end{align*}