72.8.22 problem 35

Internal problem ID [14786]
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 : 35
Date solved : Tuesday, January 28, 2025 at 07:15:23 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=2 t y+3 t \,{\mathrm e}^{t^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 17

dsolve([diff(y(t),t)= 2*t*y(t)+3*t*exp(t^2),y(0) = 1],y(t), singsol=all)
 

\[ y = \frac {\left (3 t^{2}+2\right ) {\mathrm e}^{t^{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 21

DSolve[{D[y[t],t]== 2*t*y[t]+3*t*Exp[t^2],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{t^2} \left (3 t^2+2\right ) \]