72.2.10 problem 10

Internal problem ID [14566]
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 : Thursday, March 13, 2025 at 03:34:26 AM
CAS classification : [_separable]

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

With initial conditions

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

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

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

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

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

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

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

✓ Sympy. Time used: 0.286 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(t + 1)*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 1/2} 
dsolve(ode,func=y(t),ics=ics)
 

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