60.2.120 problem 696

Internal problem ID [10707]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 696
Date solved : Monday, January 27, 2025 at 09:28:42 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 32

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

\[ y = \frac {\tan \left (\left ({\mathrm e} \left (\int \frac {x \,{\mathrm e}^{x}}{\ln \left (x -1\right )}d x \right )+c_{1} \right ) \sqrt {7}\right ) x \sqrt {7}}{7} \]

✓ Solution by Mathematica

Time used: 0.290 (sec). Leaf size: 52

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

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