Internal problem ID [8537]
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]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (-1-x^{3} x^{\frac {2}{\ln \relax (x )+1}} {\mathrm e}^{\frac {2 \ln \relax (x )^{2}}{\ln \relax (x )+1}}-x^{3} x^{\frac {2}{\ln \relax (x )+1}} {\mathrm e}^{\frac {2 \ln \relax (x )^{2}}{\ln \relax (x )+1}} \ln \relax (x )+x^{3} x^{\frac {2}{\ln \relax (x )+1}} {\mathrm e}^{\frac {2 \ln \relax (x )^{2}}{\ln \relax (x )+1}} y+2 x^{3} x^{\frac {2}{\ln \relax (x )+1}} {\mathrm e}^{\frac {2 \ln \relax (x )^{2}}{\ln \relax (x )+1}} y \ln \relax (x )+x^{3} x^{\frac {2}{\ln \relax (x )+1}} {\mathrm e}^{\frac {2 \ln \relax (x )^{2}}{\ln \relax (x )+1}} y \ln \relax (x )^{2}\right )}{\left (\ln \relax (x )+1\right ) x}=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\frac {x^{5}}{5}}}{\ln \relax (x )^{2} {\mathrm e}^{\frac {-x^{5} \ln \relax (x )-x^{5}+10 \ln \relax (x )^{2}-5 \ln \left (\ln \relax (x )+1\right ) \ln \relax (x )-5 \ln \left (\ln \relax (x )+1\right )}{5 \ln \relax (x )+5}} x^{-\frac {2 \ln \relax (x )}{\ln \relax (x )+1}}+2 \ln \relax (x ) {\mathrm e}^{\frac {-x^{5} \ln \relax (x )-x^{5}+10 \ln \relax (x )^{2}-5 \ln \left (\ln \relax (x )+1\right ) \ln \relax (x )-5 \ln \left (\ln \relax (x )+1\right )}{5 \ln \relax (x )+5}} x^{-\frac {2 \ln \relax (x )}{\ln \relax (x )+1}}+c_{1} \ln \relax (x )+{\mathrm e}^{\frac {-x^{5} \ln \relax (x )-x^{5}+10 \ln \relax (x )^{2}-5 \ln \left (\ln \relax (x )+1\right ) \ln \relax (x )-5 \ln \left (\ln \relax (x )+1\right )}{5 \ln \relax (x )+5}} x^{-\frac {2 \ln \relax (x )}{\ln \relax (x )+1}}+c_{1}} \]
✓ Solution by Mathematica
Time used: 1.545 (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*}