23.1.6 problem 1(f)

Internal problem ID [4096]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 08:08:31 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve((x+1)*diff(y(x),x)-x^2*y(x)^2=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {2}{x^{2}+2 \ln \left (x +1\right )-2 c_{1} -2 x} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 32

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

\begin{align*} y(x)\to -\frac {2}{x^2-2 x+2 \log (x+1)-3+2 c_1} \\ y(x)\to 0 \\ \end{align*}