60.2.134 problem 710

Internal problem ID [10721]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 710
Date solved : Monday, January 27, 2025 at 09:30:50 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

dsolve(diff(y(x),x) = (-ln(x)+exp(1/x)+4*x^2*y(x)+2*x+2*x*y(x)^2+2*x^3)/(ln(x)-exp(1/x)),y(x), singsol=all)
 

\[ y = -x +\tan \left (2 c_{1} +2 \left (\int \frac {x}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}}d x \right )\right ) \]

✓ Solution by Mathematica

Time used: 1.061 (sec). Leaf size: 38

DSolve[D[y[x],x] == (E^x^(-1) + 2*x + 2*x^3 - Log[x] + 4*x^2*y[x] + 2*x*y[x]^2)/(-E^x^(-1) + Log[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+\tan \left (\int _1^x-\frac {2 K[5]}{e^{\frac {1}{K[5]}}-\log (K[5])}dK[5]+c_1\right ) \]