Internal problem ID [8440]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 860.
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 )+x \cos \left (2 y\right )+\cos \left (2 y\right ) x^{3}+\cos \left (2 y\right ) x^{4}+x +x^{3}+x^{4}}{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 27
dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))+x*cos(2*y(x))+cos(2*y(x))*x^3+cos(2*y(x))*x^4+x+x^3+x^4)/x,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {4 x^{5}+5 x^{4}+10 x^{2}+c_{1}}{20 x}\right ) \]
✓ Solution by Mathematica
Time used: 5.075 (sec). Leaf size: 101
DSolve[y'[x] == (x/2 + x^3/2 + x^4/2 + (x*Cos[2*y[x]])/2 + (x^3*Cos[2*y[x]])/2 + (x^4*Cos[2*y[x]])/2 - Sin[2*y[x]]/2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcTan}\left (\frac {x^4}{5}+\frac {x^3}{4}+\frac {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*}