62.2.2 problem Ex 2

Internal problem ID [12804]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 9. Variables searated or separable. Page 13
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:21:41 AM
CAS classification : [_separable]

\begin{align*} \left (1+x \right ) y^{2}-x^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve((1+x)*y(x)^2-x^3*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {2 x^{2}}{2 c_{1} x^{2}+2 x +1} \]

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 29

DSolve[(1+x)*y[x]^2-x^3*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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