Internal problem ID [3288]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 544.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y y^{\prime } x -4 x^{2} \left (1+2 x \right )-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve(2*x*y(x)*diff(y(x),x) = 4*x^2*(1+2*x)+y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {4 x^{3}+4 x^{2}+c_{1} x} \\ y \relax (x ) = -\sqrt {4 x^{3}+4 x^{2}+c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 48
DSolve[2 x y[x] y'[x]==4 x^2(1+2 x)+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {4 x (x+1)+c_1} \\ y(x)\to \sqrt {x} \sqrt {4 x (x+1)+c_1} \\ \end{align*}