Internal problem ID [3278]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 534.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (y+x^{3}\right ) y^{\prime }-\left (-y+x^{3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.131 (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 \relax (x ) = \frac {c_{1} \left (c_{1}-\sqrt {x^{4}+c_{1}^{2}}\right )}{x} \\ y \relax (x ) = \frac {c_{1} \left (c_{1}+\sqrt {x^{4}+c_{1}^{2}}\right )}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.631 (sec). Leaf size: 72
DSolve[x(x^3+y[x])y'[x]==(x^3-y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{-1+\sqrt {\frac {1}{x^2}} x \sqrt {1+c_1 x^4}} \\ 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*}