2.41 problem 48(d)

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*}