Internal problem ID [3631]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 903.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.112 (sec). Leaf size: 32
dsolve(x^2*diff(y(x),x)^2+2*x*(2*x+y(x))*diff(y(x),x)-4*a+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{2}+a}{x} \\ y \relax (x ) = c_{1}+\frac {\frac {c_{1}^{2}}{4}-a}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.461 (sec). Leaf size: 44
DSolve[x^2 (y'[x])^2+2 x(2 x+y[x])y'[x]-4 a+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-a+c_1 (-2 x+c_1)}{x} \\ y(x)\to -2 \sqrt {a} \\ y(x)\to 2 \sqrt {a} \\ \end{align*}