15.5.5 problem 5

Internal problem ID [2941]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:59:50 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 72

dsolve((x*y(x)^3-1)+x^2*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (12 x^{2}+8 c_1 \right )^{{1}/{3}}}{2 x} \\ y &= -\frac {\left (12 x^{2}+8 c_1 \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y &= \frac {\left (12 x^{2}+8 c_1 \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.241 (sec). Leaf size: 80

DSolve[(x*y[x]^3-1)+x^2*y[x]^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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