Internal problem ID [14403]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {2 t^{5}}{5 y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve(diff(y(t),t)=2*t^5/(5*y(t)^2),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {\left (25 t^{6}+125 c_{1} \right )^{\frac {1}{3}}}{5} \\ y \left (t \right ) &= -\frac {\left (25 t^{6}+125 c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{10} \\ y \left (t \right ) &= \frac {\left (25 t^{6}+125 c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{10} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 72
DSolve[y'[t]==2*t^5/(5*y[t]^2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt [3]{-\frac {1}{5}} \sqrt [3]{t^6+15 c_1} \\ y(t)\to \sqrt [3]{\frac {t^6}{5}+3 c_1} \\ y(t)\to (-1)^{2/3} \sqrt [3]{\frac {t^6}{5}+3 c_1} \\ \end{align*}