12.2.41 problem 48(d)

Internal problem ID [1577]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 48(d)
Date solved : Monday, January 27, 2025 at 05:09:02 AM
CAS classification : [[_homogeneous, `class C`], _rational, _Riccati]

\begin{align*} \frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )}&=-\frac {3}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve(diff(y(x),x)/(1+y(x))^2-1/(x*(1+y(x)))= -3/x^2,y(x), singsol=all)
 

\[ y = -1+\frac {x}{3 \ln \left (x \right )+3 c_1} \]

✓ Solution by Mathematica

Time used: 0.254 (sec). Leaf size: 31

DSolve[D[y[x],x]/(1+y[x])^2-1/(x*(1+y[x]))== -3/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x-3 \log (x)-3 c_1}{3 (\log (x)+c_1)} \\ y(x)\to -1 \\ \end{align*}