Internal problem ID [8533]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 953.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (\ln \relax (x )+\ln \relax (y)-1+\ln \relax (x )^{2} x +2 x \ln \relax (y) \ln \relax (x )+x \ln \relax (y)^{2}+\ln \relax (x )^{2} x^{3}+2 x^{3} \ln \relax (y) \ln \relax (x )+x^{3} \ln \relax (y)^{2}+\ln \relax (x )^{2} x^{4}+2 x^{4} \ln \relax (y) \ln \relax (x )+x^{4} \ln \relax (y)^{2}\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 145
dsolve(diff(y(x),x) = y(x)*(ln(x)+ln(y(x))-1+x*ln(x)^2+2*x*ln(y(x))*ln(x)+x*ln(y(x))^2+x^3*ln(x)^2+2*x^3*ln(y(x))*ln(x)+x^3*ln(y(x))^2+x^4*ln(x)^2+2*x^4*ln(y(x))*ln(x)+x^4*ln(y(x))^2)/x,y(x), singsol=all)
\[ y \relax (x ) = x^{-\frac {4 x^{5}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} x^{-\frac {5 x^{4}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} x^{-\frac {10 x^{2}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} x^{-\frac {20 c_{1}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} {\mathrm e}^{-\frac {20 x}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} \]
✓ Solution by Mathematica
Time used: 0.503 (sec). Leaf size: 43
DSolve[y'[x] == ((-1 + Log[x] + x*Log[x]^2 + x^3*Log[x]^2 + x^4*Log[x]^2 + Log[y[x]] + 2*x*Log[x]*Log[y[x]] + 2*x^3*Log[x]*Log[y[x]] + 2*x^4*Log[x]*Log[y[x]] + x*Log[y[x]]^2 + x^3*Log[y[x]]^2 + x^4*Log[y[x]]^2)*y[x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {20 x}{4 x^5+5 x^4+10 x^2+20 c_1}}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}