72.1.23 problem 26

Internal problem ID [14623]
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 : 26
Date solved : Tuesday, January 28, 2025 at 06:44:53 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 12

dsolve([diff(y(t),t)=t*y(t),y(0) = 3],y(t), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{\frac {t^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 16

DSolve[{D[y[t],t]==t*y[t],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 e^{\frac {t^2}{2}} \]