Internal problem ID [11701]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (1+x \right ) y^{2}+y+\left (2 y x +1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve((y(x)^2*(x+1)+y(x))+(2*x*y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-1+\sqrt {{\mathrm e}^{x} \left (-4 c_{1} x +{\mathrm e}^{x}\right )}\, {\mathrm e}^{-x}}{2 x} \\ y \left (x \right ) &= \frac {-\sqrt {{\mathrm e}^{x} \left (-4 c_{1} x +{\mathrm e}^{x}\right )}\, {\mathrm e}^{-x}-1}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.638 (sec). Leaf size: 69
DSolve[(y[x]^2*(x+1)+y[x])+(2*x*y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1+\frac {\sqrt {e^x+4 c_1 x}}{\sqrt {e^x}}}{2 x} \\ y(x)\to \frac {-1+\frac {\sqrt {e^x+4 c_1 x}}{\sqrt {e^x}}}{2 x} \\ \end{align*}