Internal problem ID [3625]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 369.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {x^{4} y^{\prime }-\left (x^{3}+y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x^4*diff(y(x),x) = (x^3+y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 x^{3}}{2 c_{1} x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.141 (sec). Leaf size: 26
DSolve[x^4 y'[x]==(x^3+y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^3}{1+2 c_1 x^2} y(x)\to 0 \end{align*}