60.1.299 problem 300

Internal problem ID [10313]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 300
Date solved : Monday, January 27, 2025 at 07:08:02 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} 6 x y^{2} y^{\prime }+2 y^{3}+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 90

dsolve(6*x*y(x)^2*diff(y(x),x)+2*y(x)^3+x=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {2^{{1}/{3}} {\left (-\left (x^{2}-4 c_{1} \right ) x^{2}\right )}^{{1}/{3}}}{2 x} \\ y &= -\frac {2^{{1}/{3}} {\left (-\left (x^{2}-4 c_{1} \right ) x^{2}\right )}^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y &= \frac {2^{{1}/{3}} {\left (-\left (x^{2}-4 c_{1} \right ) x^{2}\right )}^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 99

DSolve[6*x*y[x]^2*D[y[x],x]+2*y[x]^3+x==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ \end{align*}