Internal problem ID [3375]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 635.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (a \,x^{2}+2 y x -a y^{2}\right ) y^{\prime }+x^{2}-2 a y x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
dsolve((a*x^2+2*x*y(x)-a*y(x)^2)*diff(y(x),x)+x^2-2*a*x*y(x)-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-a +\sqrt {-4 x^{2} c_{1}^{2}+a^{2}-4 c_{1} x}}{2 c_{1}} \\ y \relax (x ) = \frac {a +\sqrt {-4 x^{2} c_{1}^{2}+a^{2}-4 c_{1} x}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.73 (sec). Leaf size: 87
DSolve[(a x^2+2 x y[x]-a y[x]^2)y'[x]+x^2-2 a x y[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (a \left (-e^{c_1}\right )-\sqrt {a^2 e^{2 c_1}+4 x \left (-x+e^{c_1}\right )}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {a^2 e^{2 c_1}+4 x \left (-x+e^{c_1}\right )}-a e^{c_1}\right ) \\ \end{align*}