60.2.109 problem 685

Internal problem ID [10696]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 685
Date solved : Monday, January 27, 2025 at 09:27:59 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y+\ln \left (\left (1+x \right ) \left (x -1\right )\right ) x^{3}+7 \ln \left (\left (1+x \right ) \left (x -1\right )\right ) x y^{2}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 44

dsolve(diff(y(x),x) = (y(x)+ln((x+1)*(x-1))*x^3+7*ln((x+1)*(x-1))*x*y(x)^2)/x,y(x), singsol=all)
 

\[ y = \frac {\tan \left (\frac {\left (x^{2} \ln \left (x^{2}-1\right )-x^{2}-\ln \left (x^{2}-1\right )+2 c_{1} +1\right ) \sqrt {7}}{2}\right ) x \sqrt {7}}{7} \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 69

DSolve[D[y[x],x] == (x^3*Log[(-1 + x)*(1 + x)] + y[x] + 7*x*Log[(-1 + x)*(1 + x)]*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{7 K[1]^2+1}dK[1]=\frac {1}{2} \left (-x^2+x^2 \log (x-1)+x^2 \log (x+1)-\log (1-x)-\log (x+1)\right )+c_1,y(x)\right ] \]