Internal problem ID [8535]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 957.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-\frac {y \left (-1-x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}}-x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} \ln \left (x \right )+x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y+2 x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y \ln \left (x \right )+x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y \ln \left (x \right )^{2}\right )}{\left (\ln \left (x \right )+1\right ) x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 197
dsolve(diff(y(x),x) = 1/(1+ln(x))*y(x)*(-1-x^3*x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)-x^3*x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*ln(x)+x^3*x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*y(x)+2*x^3*x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*y(x)*ln(x)+x^3*x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*y(x)*ln(x)^2)/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\frac {x^{5}}{5}}}{\ln \left (x \right )^{2} x^{-\frac {2 \ln \left (x \right )}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {-\ln \left (x \right ) x^{5}-x^{5}+10 \ln \left (x \right )^{2}-5 \ln \left (\ln \left (x \right )+1\right ) \ln \left (x \right )-5 \ln \left (\ln \left (x \right )+1\right )}{5 \ln \left (x \right )+5}}+2 \ln \left (x \right ) x^{-\frac {2 \ln \left (x \right )}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {-\ln \left (x \right ) x^{5}-x^{5}+10 \ln \left (x \right )^{2}-5 \ln \left (\ln \left (x \right )+1\right ) \ln \left (x \right )-5 \ln \left (\ln \left (x \right )+1\right )}{5 \ln \left (x \right )+5}}+c_{1} \ln \left (x \right )+x^{-\frac {2 \ln \left (x \right )}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {-\ln \left (x \right ) x^{5}-x^{5}+10 \ln \left (x \right )^{2}-5 \ln \left (\ln \left (x \right )+1\right ) \ln \left (x \right )-5 \ln \left (\ln \left (x \right )+1\right )}{5 \ln \left (x \right )+5}}+c_{1}} \]
✓ Solution by Mathematica
Time used: 1.955 (sec). Leaf size: 32
DSolve[y'[x] == (y[x]*(-1 - E^((2*Log[x]^2)/(1 + Log[x]))*x^(3 + 2/(1 + Log[x])) - E^((2*Log[x]^2)/(1 + Log[x]))*x^(3 + 2/(1 + Log[x]))*Log[x] + E^((2*Log[x]^2)/(1 + Log[x]))*x^(3 + 2/(1 + Log[x]))*y[x] + 2*E^((2*Log[x]^2)/(1 + Log[x]))*x^(3 + 2/(1 + Log[x]))*Log[x]*y[x] + E^((2*Log[x]^2)/(1 + Log[x]))*x^(3 + 2/(1 + Log[x]))*Log[x]^2*y[x]))/(x*(1 + Log[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{c_1 e^{\frac {x^5}{5}} (\log (x)+1)+\log (x)+1} \\ y(x)\to 0 \\ \end{align*}