Internal problem ID [12404]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number: 9 (e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-3 x y^{\frac {1}{3}}=0} \] With initial conditions \begin {align*} [y \left (-1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 7
dsolve([diff(y(x),x)=3*x*y(x)^(1/3),y(-1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = x^{3} \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 67
DSolve[{y'[x]==3*x*y[x]^(1/3),{y[-1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (2 x^2-i \sqrt {3}-3\right )^{3/2}}{2 \sqrt {2}} y(x)\to \frac {\left (2 x^2+i \sqrt {3}-3\right )^{3/2}}{2 \sqrt {2}} \end{align*}