Internal problem ID [972]
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: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3 x \left (y-1\right )^{\frac {1}{3}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 5
dsolve([diff(y(x),x)=3*x*(y(x)-1)^(1/3),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = 1 \]
✓ Solution by Mathematica
Time used: 0.29 (sec). Leaf size: 19
DSolve[{y'[x]==3*x*(y[x]-1)^(1/3),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1 \\ y(x)\to \left (x^2\right )^{3/2}+1 \\ \end{align*}