29.23.22 problem 653

Internal problem ID [5244]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 653
Date solved : Monday, January 27, 2025 at 10:49:04 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} 3 x y^{2} y^{\prime }&=2 x -y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 71

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

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

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 72

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

\begin{align*} y(x)\to \frac {\sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ \end{align*}