64.7.3 problem 3

Internal problem ID [13377]
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
Date solved : Tuesday, January 28, 2025 at 05:36:06 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.006 (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 &= \frac {-\sqrt {{\mathrm e}^{x} \left (-4 c_{1} x +{\mathrm e}^{x}\right )}\, {\mathrm e}^{-x}-1}{2 x} \\ y &= \frac {-1+\sqrt {{\mathrm e}^{x} \left (-4 c_{1} x +{\mathrm e}^{x}\right )}\, {\mathrm e}^{-x}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.044 (sec). Leaf size: 77

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

\begin{align*} y(x)\to -\frac {1+\frac {\sqrt {e^{x+1}+4 c_1 x}}{\sqrt {e^{x+1}}}}{2 x} \\ y(x)\to \frac {-1+\frac {\sqrt {e^{x+1}+4 c_1 x}}{\sqrt {e^{x+1}}}}{2 x} \\ \end{align*}