29.12.27 problem 346

Internal problem ID [4946]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 346
Date solved : Monday, January 27, 2025 at 09:53:19 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(x^3*diff(y(x),x) = y(x)*(x^2+y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 22

DSolve[x^3 D[y[x],x]==y[x](x^2+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2}{1+c_1 x} \\ y(x)\to 0 \\ \end{align*}