12.4.16 problem 19

Internal problem ID [1623]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:14:26 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=9 \end{align*}

✓ Solution by Maple

Time used: 0.107 (sec). Leaf size: 26

dsolve([diff(y(x),x)=3*x*(y(x)-1)^(1/3),y(0) = 9],y(x), singsol=all)
 

\[ y = x^{2} \sqrt {x^{2}+4}+4 \sqrt {x^{2}+4}+1 \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 16

DSolve[{D[y[x],x]==3*x*(y[x]-1)^(1/3),y[0]==9},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2+4\right )^{3/2}+1 \]