Internal problem ID [974]
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).
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 (3) = -7] \end {align*}
✓ Solution by Maple
Time used: 0.142 (sec). Leaf size: 19
dsolve([diff(y(x),x)=3*x*(y(x)-1)^(1/3),y(3) = -7],y(x), singsol=all)
\[ y \relax (x ) = 1+\left (-11+2 i \sqrt {3}+x^{2}\right )^{\frac {3}{2}} \]
✓ Solution by Mathematica
Time used: 0.139 (sec). Leaf size: 49
DSolve[{y'[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*}