Internal problem ID [7702]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 122.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x y^{\prime }+\left (\sin \relax (y)-3 x^{2} \cos \relax (y)\right ) \cos \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 16
dsolve(x*diff(y(x),x) + (sin(y(x))-3*x^2*cos(y(x)))*cos(y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {x^{3}+2 c_{1}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 3.995 (sec). Leaf size: 85
DSolve[x*y'[x] + (Sin[y[x]]-3*x^2*Cos[y[x]])*Cos[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \operatorname {ArcTan}\left (x^2+\frac {c_1}{2 x}\right ) \\ y(x)\to -\frac {1}{2} i \left (\log \left (-\frac {i}{2 x}\right )-\log \left (\frac {i}{2 x}\right )\right ) \\ y(x)\to \frac {1}{2} i \left (\log \left (-\frac {i}{2 x}\right )-\log \left (\frac {i}{2 x}\right )\right ) \\ \end{align*}