Internal problem ID [11166]
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]
\[ \boxed {y^{2}+2 y m x +\left (y^{2} m -m \,x^{2}-2 y x \right ) y^{\prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (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 \left (x \right ) &= \frac {m -\sqrt {-4 c_{1}^{2} x^{2}-4 c_{1} x +m^{2}}}{2 c_{1}} \\ y \left (x \right ) &= \frac {m +\sqrt {-4 c_{1}^{2} x^{2}-4 c_{1} x +m^{2}}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.604 (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*}