Internal problem ID [8502]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 924.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
\[ \boxed {y^{\prime }+\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-f_{1} \left (x \right )\right ) y}{\ln \left (y\right )}=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 47
dsolve(diff(y(x),x) = -(-1/2*ln(y(x))^2/x-_F1(x))/ln(y(x))*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = {\mathrm e}^{\sqrt {2 \left (\int \frac {f_{1} \left (x \right )}{x}d x \right ) x +2 x c_{1}}} \\ y \left (x \right ) = {\mathrm e}^{-\sqrt {2 \left (\int \frac {f_{1} \left (x \right )}{x}d x \right ) x +2 x c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.31 (sec). Leaf size: 79
DSolve[y'[x] == ((F1[x] + Log[y[x]]^2/(2*x))*y[x])/Log[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^x\left (-\frac {\log ^2(y(x))}{2 K[1]^2}-\frac {\text {F1}(K[1])}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (\frac {\log (K[2])}{x K[2]}-\int _1^x-\frac {\log (K[2])}{K[1]^2 K[2]}dK[1]\right )dK[2]=c_1,y(x)\right ] \]