13.15 problem 369

Internal problem ID [3117]

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]

Solve \begin {gather*} \boxed {x^{4} y^{\prime }-\left (y+x^{3}\right ) y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 19

dsolve(x^4*diff(y(x),x) = (x^3+y(x))*y(x),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {2 x^{3}}{2 c_{1} x^{2}+1} \]

Solution by Mathematica

Time used: 0.134 (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*}