Internal problem ID [12402]
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 (c).
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*} \left [y \left (-1\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 20
dsolve([diff(y(x),x)=3*x*y(x)^(1/3),y(-1) = 1/2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 x^{2}+2^{\frac {1}{3}}-2\right ) \sqrt {4 x^{2}+2 \,2^{\frac {1}{3}}-4}}{4} \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 30
DSolve[{y'[x]==3*x*y[x]^(1/3),{y[-1]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (2 x^2+\sqrt [3]{2}-2\right )^{3/2}}{2 \sqrt {2}} \]