29.13.15 problem 369

Internal problem ID [4969]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 369
Date solved : Monday, January 27, 2025 at 10:00:15 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x^{4} y^{\prime }&=\left (x^{3}+y\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.005 (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: 0.163 (sec). Leaf size: 26

DSolve[x^4 D[y[x],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*}