12.4.17 problem 20(a)

Internal problem ID [1624]
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 : 20(a)
Date solved : Monday, January 27, 2025 at 05:14:48 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 (3\right )&=-7 \end{align*}

✓ Solution by Maple

Time used: 0.112 (sec). Leaf size: 18

dsolve([diff(y(x),x)=3*x*(y(x)-1)^(1/3),y(3) = -7],y(x), singsol=all)
 

\[ y = 1+\left (-11+2 i \sqrt {3}+x^{2}\right )^{{3}/{2}} \]

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 49

DSolve[{D[y[x],x]==3*x*(y[x]-1)^(1/3),y[3]==-7},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1+\left (x^2-2 i \sqrt {3}-11\right )^{3/2} \\ y(x)\to 1+\left (x^2+2 i \sqrt {3}-11\right )^{3/2} \\ \end{align*}