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