Internal problem ID [3760]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 508.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {y y^{\prime } x -y^{2}=-x^{4}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(x*y(x)*diff(y(x),x)+x^4-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {-x^{2}+c_{1}}\, x y \left (x \right ) = -\sqrt {-x^{2}+c_{1}}\, x \end{align*}
✓ Solution by Mathematica
Time used: 0.425 (sec). Leaf size: 43
DSolve[x y[x] y'[x]+x^4-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^4+c_1 x^2} y(x)\to \sqrt {-x^4+c_1 x^2} \end{align*}