60.1.316 problem 317

Internal problem ID [10330]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 317
Date solved : Monday, January 27, 2025 at 07:13:10 PM
CAS classification : [_rational]

\begin{align*} \left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }+y^{2}-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve((2*x*y(x)^3+x*y(x)+x^2)*diff(y(x),x)+y(x)^2-x*y(x) = 0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 23

DSolve[-(x*y[x]) + y[x]^2 + (x^2 + x*y[x] + 2*x*y[x]^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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