15.8.19 problem 19

Internal problem ID [3022]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 19
Date solved : Monday, January 27, 2025 at 07:09:04 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 73

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

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

✓ Solution by Mathematica

Time used: 0.442 (sec). Leaf size: 80

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

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