Internal problem ID [9290]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 956.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-\frac {y \left (-1-x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2}-x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} \ln \left (x \right )+x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y+2 x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y \ln \left (x \right )+x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (\ln \left (x \right )+1\right ) x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x) = 1/(1+ln(x))*y(x)*(-1-x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*x^2-x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*x^2*ln(x)+x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*x^2*y(x)+2*x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*x^2*y(x)*ln(x)+x^(2/(1+ln(x)))*exp(2/(1+ln(x))*ln(x)^2)*x^2*y(x)*ln(x)^2)/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\frac {x^{4}}{4}}}{\left (\ln \left (x \right )+1\right ) \left ({\mathrm e}^{-\frac {x^{4}}{4}}+c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 1.904 (sec). Leaf size: 33
DSolve[y'[x] == (y[x]*(-1 - E^((2*Log[x]^2)/(1 + Log[x]))*x^(2 + 2/(1 + Log[x])) - E^((2*Log[x]^2)/(1 + Log[x]))*x^(2 + 2/(1 + Log[x]))*Log[x] + E^((2*Log[x]^2)/(1 + Log[x]))*x^(2 + 2/(1 + Log[x]))*y[x] + 2*E^((2*Log[x]^2)/(1 + Log[x]))*x^(2 + 2/(1 + Log[x]))*Log[x]*y[x] + E^((2*Log[x]^2)/(1 + Log[x]))*x^(2 + 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}{\left (1+c_1 e^{\frac {x^4}{4}}\right ) (\log (x)+1)} \\ y(x)\to 0 \\ \end{align*}