38.2.20 problem 20

Internal problem ID [6449]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:04:30 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 38

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

\[ y = \frac {{\mathrm e}^{\operatorname {RootOf}\left (-2 \ln \left (x \right ) {\mathrm e}^{2 \textit {\_Z}}+2 c_1 \,{\mathrm e}^{2 \textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}}-1\right )}}{x} \]

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 28

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

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