10.2 problem Ex 2

Internal problem ID [10149]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]

Solve \begin {gather*} \boxed {2 x +\left (x^{2}+y^{2}+2 y\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

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

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

Solution by Mathematica

Time used: 0.181 (sec). Leaf size: 24

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

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