12.5.26 problem 23

Internal problem ID [1650]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 23
Date solved : Monday, January 27, 2025 at 05:16:14 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 14

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

\[ y = \left (3 \ln \left (x \right )+27\right )^{{1}/{3}} x \]

✓ Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 20

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

\[ y(x)\to \sqrt [3]{3} x \sqrt [3]{\log (x)+9} \]