29.24.11 problem 673

Internal problem ID [5264]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 673
Date solved : Monday, January 27, 2025 at 10:50:43 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (1-y x \right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.189 (sec). Leaf size: 34

dsolve(x*(1-x*y(x))^2*diff(y(x),x)+(1+x^2*y(x)^2)*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 25

DSolve[x(1-x y[x])^2 D[y[x],x]+(1+x^2 y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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