Internal problem ID [10152]
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 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{2}-x^{2}+2 y m x +\left (y^{2} m -m \,x^{2}-2 y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
dsolve((y(x)^2-x^2+2*m*x*y(x))+(m*y(x)^2-m*x^2-2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-m +\sqrt {-4 x^{2} c_{1}^{2}+m^{2}-4 x c_{1}}}{2 c_{1}} \\ y \relax (x ) = \frac {m +\sqrt {-4 x^{2} c_{1}^{2}+m^{2}-4 x c_{1}}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.692 (sec). Leaf size: 89
DSolve[(y[x]^2-x^2+2*m*x*y[x])+(m*y[x]^2-m*x^2-2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-\sqrt {e^{2 c_1} m^2-4 x^2+4 e^{c_1} x}-e^{c_1} m\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {e^{2 c_1} m^2-4 x^2+4 e^{c_1} x}-e^{c_1} m\right ) \\ \end{align*}