72.8.9 problem 22

Internal problem ID [14773]
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. Review Exercises for chapter 1. page 136
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 07:14:56 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

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

\[ y = c_{1} {\mathrm e}^{\frac {t^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 22

DSolve[D[y[t],t]==t*y[t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to c_1 e^{\frac {t^2}{2}} \\ y(t)\to 0 \\ \end{align*}