Internal problem ID [5270]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 23 (o).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {y^{2}-\frac {y}{x \left (x +y\right )}+\left (\frac {1}{x +y}+2 \left (1+x \right ) y\right ) y^{\prime }=-2} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 130
dsolve((y(x)^2- y(x)/(x*(x+y(x)))+2)+( 1/(x+y(x)) + 2*y(x)*(1+x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \left (-x \,{\mathrm e}^{\operatorname {RootOf}\left (x^{3} {\mathrm e}^{2 \textit {\_Z}}+x^{2} {\mathrm e}^{2 \textit {\_Z}}-2 x^{3} {\mathrm e}^{\textit {\_Z}}+c_{1} {\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}-2 x^{2} {\mathrm e}^{\textit {\_Z}}+x^{3}+x^{2}\right )}+x \right ) {\mathrm e}^{-\operatorname {RootOf}\left (x^{3} {\mathrm e}^{2 \textit {\_Z}}+x^{2} {\mathrm e}^{2 \textit {\_Z}}-2 x^{3} {\mathrm e}^{\textit {\_Z}}+c_{1} {\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}-2 x^{2} {\mathrm e}^{\textit {\_Z}}+x^{3}+x^{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.43 (sec). Leaf size: 29
DSolve[(y[x]^2- y[x]/(x*(x+y[x]))+2)+( 1/(x+y[x]) + 2*y[x]*(1+x))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x y(x)^2+y(x)^2+\log (y(x)+x)+2 x-\log (x)=c_1,y(x)\right ] \]