29.25.12 problem 709

Internal problem ID [5299]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 709
Date solved : Monday, January 27, 2025 at 11:05:02 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 2 \left (x -y^{4}\right ) y^{\prime }&=y \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 89

dsolve(2*(x-y(x)^4)*diff(y(x),x) = y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {2 \sqrt {c_{1}^{2}-4 x}+2 c_{1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.150 (sec). Leaf size: 128

DSolve[2(x-y[x]^4)D[y[x],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*}