Internal problem ID [927]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _Riccati]
\[ \boxed {\frac {y^{\prime }}{\left (1+y\right )^{2}}-\frac {1}{x \left (1+y\right )}=-\frac {3}{x^{2}}} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = -1+\frac {x}{3 \ln \left (x \right )+3 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 31
DSolve[y'[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*}