Internal problem ID [3019]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 271.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-2 y \left (x -y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(x^2*diff(y(x),x) = 2*y(x)*(x-y(x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {3 x^{2}}{\sqrt {12 x^{3}+9 c_{1}}} \\ y \relax (x ) = \frac {3 x^{2}}{\sqrt {12 x^{3}+9 c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.214 (sec). Leaf size: 51
DSolve[x^2 y'[x]==2 y[x](x-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}} \\ y(x)\to \frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}} \\ y(x)\to 0 \\ \end{align*}