Internal problem ID [8253]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 673.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 17
dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))+cos(2*y(x))*x^2+x^2)/x,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {x^{3}+6 c_{1}}{3 x}\right ) \]
✓ Solution by Mathematica
Time used: 3.74 (sec). Leaf size: 87
DSolve[y'[x] == (x^2/2 + (x^2*Cos[2*y[x]])/2 - Sin[2*y[x]]/2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cot ^{-1}\left (\frac {6 x}{2 x^3+3 c_1}\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*}