29.25.9 problem 706

Internal problem ID [5296]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 706
Date solved : Monday, January 27, 2025 at 11:04:50 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.188 (sec). Leaf size: 97

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

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

✓ Solution by Mathematica

Time used: 2.171 (sec). Leaf size: 122

DSolve[(x^2-y[x]^4)D[y[x],x]==x y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to \sqrt {-\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to -\sqrt {\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to \sqrt {\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to 0 \\ \end{align*}