Internal problem ID [3699]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 974.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}-4 y y^{\prime } a +4 a^{2}-4 a x +y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 113
dsolve(y(x)^2*diff(y(x),x)^2-4*a*y(x)*diff(y(x),x)+4*a^2-4*a*x+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -2 \sqrt {a x} \\ y \relax (x ) = 2 \sqrt {a x} \\ y \relax (x ) = -\frac {\sqrt {-16 a^{4}+32 a^{3} x -16 a^{2} x^{2}+8 c_{1} a^{2}+8 a x c_{1}-c_{1}^{2}}}{4 a} \\ y \relax (x ) = \frac {\sqrt {-16 a^{4}+32 a^{3} x -16 a^{2} x^{2}+8 c_{1} a^{2}+8 a x c_{1}-c_{1}^{2}}}{4 a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.65 (sec). Leaf size: 83
DSolve[y[x]^2 (y'[x])^2-4 a y[x] y'[x]+4 a^2-4 a x+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {4 a^2 x (4 a-x)-4 a c_1 x-c_1{}^2}}{2 a} \\ y(x)\to \frac {\sqrt {4 a^2 x (4 a-x)-4 a c_1 x-c_1{}^2}}{2 a} \\ \end{align*}