Internal problem ID [3447]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 709.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {2 \left (x -y^{4}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 89
dsolve(2*(x-y(x)^4)*diff(y(x),x) = y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ y \relax (x ) = -\frac {\sqrt {2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ y \relax (x ) = \frac {\sqrt {2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.098 (sec). Leaf size: 128
DSolve[2(x-y[x]^4)y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {c_1-\sqrt {-4 x+c_1{}^2}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {c_1-\sqrt {-4 x+c_1{}^2}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {-4 x+c_1{}^2}+c_1}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\sqrt {-4 x+c_1{}^2}+c_1}}{\sqrt {2}} \\ y(x)\to 0 \\ \end{align*}