29.10.5 problem 271

Internal problem ID [4871]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 271
Date solved : Monday, January 27, 2025 at 09:45:47 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

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

\begin{align*} y \left (x \right ) &= -\frac {3 x^{2}}{\sqrt {12 x^{3}+9 c_{1}}} \\ y \left (x \right ) &= \frac {3 x^{2}}{\sqrt {12 x^{3}+9 c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 51

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

\begin{align*} y(x)\to -\frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}} \\ y(x)\to \frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}} \\ y(x)\to 0 \\ \end{align*}