Internal problem ID [12553]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.2. page
33
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t}{y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t)=t/y(t),y(t), singsol=all)
\begin{align*} y \left (t \right ) = \sqrt {t^{2}+c_{1}} y \left (t \right ) = -\sqrt {t^{2}+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 35
DSolve[y'[t]==t/y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {t^2+2 c_1} y(t)\to \sqrt {t^2+2 c_1} \end{align*}