Internal problem ID [10126]
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 12. Equations of
form \(y f_1(x y)+x f_2( xy) y'=0\). Page 18
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y+2 y^{2} x -x^{2} y^{3}+2 y^{\prime } y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((y(x)+2*x*y(x)^2-x^2*y(x)^3)+(2*x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {\tanh \left (-\frac {\ln \relax (x )}{2}+\frac {c_{1}}{2}\right )}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.492 (sec). Leaf size: 71
DSolve[(y[x]+2*x*y[x]^2-x^2*y[x]^3)+(2*x^2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to \frac {i \tan \left (\frac {1}{2} i \log (x)+c_1\right )}{x} \\ y(x)\to 0 \\ y(x)\to \frac {-x+e^{2 i \text {Interval}[\{0,\pi \}]}}{x^2+x e^{2 i \text {Interval}[\{0,\pi \}]}} \\ \end{align*}