72.1.9 problem 12

Internal problem ID [14609]
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
Date solved : Tuesday, January 28, 2025 at 06:44:23 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t}{y} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(t),t)=t/y(t),y(t), singsol=all)
 

\begin{align*} y &= \sqrt {t^{2}+c_{1}} \\ y &= -\sqrt {t^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 35

DSolve[D[y[t],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*}