32.6.44 problem Exercise 12.44, page 103

Internal problem ID [5909]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.44, page 103
Date solved : Monday, January 27, 2025 at 01:26:50 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.235 (sec). Leaf size: 34

dsolve((x*y(x)-1)^2*x*diff(y(x),x)+(x^2*y(x)^2+1)*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: 0.108 (sec). Leaf size: 25

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

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