29.7.13 problem 188

Internal problem ID [4788]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 188
Date solved : Monday, January 27, 2025 at 09:37:56 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y \left (1-x y^{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(x*diff(y(x),x)+(1-x*y(x)^2)*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {x \left (c_{1} x +2\right )}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {x \left (c_{1} x +2\right )}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.454 (sec). Leaf size: 40

DSolve[x D[y[x],x]+(1-x y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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