83.7.2 problem 2 (a)

Internal problem ID [19120]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (F) at page 24
Problem number : 2 (a)
Date solved : Tuesday, January 28, 2025 at 12:58:30 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{4} y^{4}+x^{2} y^{2}+y x \right ) y+\left (x^{4} y^{4}-x^{2} y^{2}+y x \right ) x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 38

dsolve((x^4*y(x)^4+x^2*y(x)^2+x*y(x))*y(x)+(x^4*y(x)^4-x^2*y(x)^2+x*y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-4 \ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+4 c_{1} {\mathrm e}^{\textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +2\right )}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.233 (sec). Leaf size: 40

DSolve[(x^4*y[x]^4+x^2*y[x]^2+x*y[x])*y[x]+(x^4*y[x]^4-x^2*y[x]^2+x*y[x])*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 0 \\ \text {Solve}\left [\frac {1}{2} x^2 y(x)^2-\frac {1}{x y(x)}-\log (y(x))+\log (x)&=c_1,y(x)\right ] \\ \end{align*}