Internal problem ID [8974]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 639.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 46
dsolve(diff(y(x),x) = (-ln(ln(y(x)))+ln(x))^2*y(x),y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{\textit {\_a} \left (x \ln \left (x \right )^{2}-2 \ln \left (x \right ) \ln \left (\ln \left (\textit {\_a} \right )\right ) x +\ln \left (\ln \left (\textit {\_a} \right )\right )^{2} x -\ln \left (\textit {\_a} \right )\right )}d \textit {\_a} -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 53
DSolve[y'[x] == (Log[x] - Log[Log[y[x]]])^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] \left (x \log ^2(x)-2 x \log (\log (K[1])) \log (x)+x \log ^2(\log (K[1]))-\log (K[1])\right )}dK[1]=\log (x)+c_1,y(x)\right ] \]