Internal problem ID [11150]
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]
\[ \boxed {y+2 y^{2} x -y^{3} x^{2}+2 y^{\prime } y x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = 0 y \left (x \right ) = \frac {\tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )}{x} \end{align*}
✓ Solution by Mathematica
Time used: 1.44 (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*}