60.1.256 problem 257

Internal problem ID [10270]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 257
Date solved : Tuesday, January 28, 2025 at 04:26:38 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (y x +x^{4}-1\right ) y^{\prime }-y \left (y x -x^{4}-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 98

dsolve(x*(x*y(x)+x^4-1)*diff(y(x),x)-y(x)*(x*y(x)-x^4-1)=0,y(x), singsol=all)
 

\[ y = \frac {\left (-c_{1} +{\mathrm e}^{\operatorname {RootOf}\left (-2 \textit {\_Z} \,x^{4} {\mathrm e}^{2 \textit {\_Z}}+2 x^{4} {\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} c_{1} x^{4}+{\mathrm e}^{2 \textit {\_Z}}-2 c_{1} {\mathrm e}^{\textit {\_Z}}+c_{1}^{2}\right )}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (-2 \textit {\_Z} \,x^{4} {\mathrm e}^{2 \textit {\_Z}}+2 x^{4} {\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} c_{1} x^{4}+{\mathrm e}^{2 \textit {\_Z}}-2 c_{1} {\mathrm e}^{\textit {\_Z}}+c_{1}^{2}\right )}}{x} \]

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 39

DSolve[x*(x*y[x]+x^4-1)*D[y[x],x]-y[x]*(x*y[x]-x^4-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 x^2+\frac {y(x)}{x}+\frac {x \left (-2 \log \left (\frac {1}{1-x y(x)}\right )-2+c_1\right )}{y(x)}=0,y(x)\right ] \]