29.19.21 problem 534

Internal problem ID [5130]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 534
Date solved : Monday, January 27, 2025 at 10:13:33 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (x^{3}+y\right ) y^{\prime }&=\left (x^{3}-y\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.859 (sec). Leaf size: 41

dsolve(x*(x^3+y(x))*diff(y(x),x) = (x^3-y(x))*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.861 (sec). Leaf size: 73

DSolve[x(x^3+y[x])D[y[x],x]==(x^3-y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^4}{-x+\frac {\sqrt {1+c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to -\frac {x^4}{x+\frac {\sqrt {1+c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to 0 \\ \end{align*}