Internal problem ID [4597]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y \left (x y+1\right )+x \left (1+x y+x^{2} y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {RootOf}\left (-2 \ln \left (x \right ) {\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{2 \textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}}-1\right )}}{x} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 30
DSolve[y[x]*(x*y[x]+1)+x*(1+x*y[x]+x^2*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {-\frac {1}{2 x^2}-\frac {y(x)}{x}}{y(x)^2}+\log (y(x))=c_1,y(x)\right ] \]