Internal problem ID [8398]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 820.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+x^{2} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve(diff(y(x),x) = 1/2*(-2*cos(y(x))+x^2*cos(2*y(x))*ln(x)+x^2*ln(x))/sin(y(x))/ln(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {arcsec}\left (\frac {2 \ln \left (x \right ) x^{2}-x^{2}+8 c_{1}}{4 \ln \left (x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 1.403 (sec). Leaf size: 73
DSolve[y'[x] == (Csc[y[x]]*(-Cos[y[x]] + (x^2*Log[x])/2 + (x^2*Cos[2*y[x]]*Log[x])/2))/(x*Log[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arccos \left (-\frac {4 \log (x)}{x^2-2 x^2 \log (x)+4 c_1}\right ) \\ y(x)\to \arccos \left (-\frac {4 \log (x)}{x^2-2 x^2 \log (x)+4 c_1}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}