60.2.159 problem 735

Internal problem ID [10746]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 735
Date solved : Monday, January 27, 2025 at 09:39:43 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`], [_Abel, `2nd type`, `class C`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 78

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

\[ y = \frac {71 \operatorname {RootOf}\left (-82944 \left (\int _{}^{\textit {\_Z}}\frac {1}{5041 \textit {\_a}^{3}-27648 \textit {\_a} +27648}d \textit {\_a} \right )-16 \ln \left (x \right )+3 c_{1} \right )-120}{\left (142 \ln \left (x \right )-71\right ) \operatorname {RootOf}\left (-82944 \left (\int _{}^{\textit {\_Z}}\frac {1}{5041 \textit {\_a}^{3}-27648 \textit {\_a} +27648}d \textit {\_a} \right )-16 \ln \left (x \right )+3 c_{1} \right )-240 \ln \left (x \right )+48} \]

✓ Solution by Mathematica

Time used: 0.560 (sec). Leaf size: 120

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

\[ \text {Solve}\left [\int _1^{\frac {(2-10 \log (x)) y(x)+5}{\sqrt [3]{142} \sqrt [3]{-\frac {1}{(2 \log (x)-1)^3}} (2 \log (x)-1) ((2 \log (x)-1) y(x)-1)}}\frac {1}{K[1]^3+\frac {24 \sqrt [3]{-2} K[1]}{71^{2/3}}+1}dK[1]+\frac {1}{9} 142^{2/3} \log (x) \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2=c_1,y(x)\right ] \]