Internal problem ID [13840]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2} y^{\prime }=-\frac {1}{2 \sqrt {t}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 73
dsolve(1/2/t^(1/2)+y(t)^2*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y = \left (-3 \sqrt {t}+c_{1} \right )^{\frac {1}{3}} y = -\frac {\left (-3 \sqrt {t}+c_{1} \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-3 \sqrt {t}+c_{1} \right )^{\frac {1}{3}}}{2} y = -\frac {\left (-3 \sqrt {t}+c_{1} \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-3 \sqrt {t}+c_{1} \right )^{\frac {1}{3}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 1.899 (sec). Leaf size: 79
DSolve[1/2/t^(1/2)+y[t]^2*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt [3]{-3} \sqrt [3]{-\sqrt {t}+c_1} y(t)\to \sqrt [3]{3} \sqrt [3]{-\sqrt {t}+c_1} y(t)\to (-1)^{2/3} \sqrt [3]{3} \sqrt [3]{-\sqrt {t}+c_1} \end{align*}