60.2.111 problem 687

Internal problem ID [10698]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 687
Date solved : Monday, January 27, 2025 at 09:28:06 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 39

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

\[ y = -\tanh \left (\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}+c_{1} +x -1\right ) x \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 69

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{(K[1]-1) (K[1]+1)}dK[1]=\frac {1}{2} \left (x^2 (-\log (x-1))+x^2 \log (x+1)+2 x+\log (1-x)-\log (x+1)\right )+c_1,y(x)\right ] \]