72.2.10 problem 10

Internal problem ID [14645]
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 1.3 page 47
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:46:02 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (1+t \right ) y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 19

DSolve[{D[y[t],t]==(t+1)*y[t],{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
 

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