60.2.119 problem 695

Internal problem ID [10706]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 695
Date solved : Monday, January 27, 2025 at 09:28:39 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

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

\[ y = \tan \left (-\operatorname {Ei}_{1}\left (-3 \ln \left (x -1\right )\right )-3 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x -1\right )\right )-2 \,\operatorname {Ei}_{1}\left (-\ln \left (x -1\right )\right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 48

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

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