77.1.20 problem 36 (page 40)

Internal problem ID [17910]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 36 (page 40)
Date solved : Tuesday, January 28, 2025 at 11:12:11 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 23

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

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