Internal problem ID [4139]
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)]`]]
\[ \boxed {x^{2} {y^{\prime }}^{2}+2 x \left (y+2 x \right ) y^{\prime }+y^{2}=4 a} \]
✓ Solution by Maple
Time used: 0.063 (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 \left (x \right ) = -\frac {x^{2}+a}{x} y \left (x \right ) = c_{1} +\frac {\frac {c_{1}^{2}}{4}-a}{x} \end{align*}
✓ Solution by Mathematica
Time used: 1.286 (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*}