Internal problem ID [13837]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\frac {t}{y}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(t),t)=-t/y(t),y(0) = 1/2],y(t), singsol=all)
\[ y = \frac {\sqrt {-4 t^{2}+1}}{2} \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 20
DSolve[{y'[t]==-t/y[t],{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \sqrt {1-4 t^2} \]