83.22.25 problem 25

Internal problem ID [19279]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (E) at page 63
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 01:22:13 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 42

dsolve((x^3*y(x)^3+x^2*y(x)^2+x*y(x)+1)*y(x)+(x^3*y(x)^3-x^2*y(x)^2-x*y(x)+1)*x*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {1}{x} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (-2 \ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +1\right )}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 35

DSolve[(x^3*y[x]^3+x^2*y[x]^2+x*y[x]+1)*y[x]+(x^3*y[x]^3-x^2*y[x]^2-x*y[x]+1)*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{x} \\ \text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))&=c_1,y(x)\right ] \\ \end{align*}