62.10.2 problem Ex 2

Internal problem ID [12839]
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 17. Other forms which Integrating factors can be found. Page 25
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:26:27 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 17

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

\[ \left (x^{2}+y^{2}\right ) {\mathrm e}^{y}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 24

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

\[ \text {Solve}\left [x^2 e^{y(x)}+e^{y(x)} y(x)^2=c_1,y(x)\right ] \]