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]
Solve \begin {gather*} \boxed {\frac {y^{\prime }}{\left (1+y\right )^{2}}-\frac {1}{x \left (1+y\right )}+\frac {3}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(diff(y(x),x)/(1+y(x))^2-1/(x*(1+y(x)))= -3/x^2,y(x), singsol=all)
\[ y \relax (x ) = -1+\frac {x}{3 \ln \relax (x )+3 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 24
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 -1+\frac {x}{3 (\log (x)+c_1)} \\ y(x)\to -1 \\ \end{align*}