76.5.3 problem 3

Internal problem ID [17423]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 10:06:46 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.071 (sec). Leaf size: 22

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

\[ y = \sqrt {3}\, \sqrt {-\frac {1}{\operatorname {LambertW}\left (-3 c_{1} x^{4}\right )}}\, x \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 65

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

\begin{align*} y(x)\to -\frac {i \sqrt {3} x}{\sqrt {W\left (-3 e^{-3-2 c_1} x^4\right )}} \\ y(x)\to \frac {i \sqrt {3} x}{\sqrt {W\left (-3 e^{-3-2 c_1} x^4\right )}} \\ \end{align*}