Internal problem ID [21]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.3. Slope fields and solution curves. Page 26
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{\frac {1}{3}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 13
dsolve([diff(y(x),x) = y(x)^(1/3),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (2 x +3\right ) \sqrt {6 x +9}}{9} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 23
DSolve[{y'[x] == y[x]^(1/3),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(2 x+3)^{3/2}}{3 \sqrt {3}} \\ \end{align*}