76.2.31 problem 31

Internal problem ID [17296]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 31
Date solved : Monday, March 31, 2025 at 03:49:50 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 21

ode:=diff(y(t),t)-3/2*y(t) = 3*t+3*exp(t); 
ic:=y(0) = y__0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -2 t -\frac {4}{3}-6 \,{\mathrm e}^{t}+{\mathrm e}^{\frac {3 t}{2}} \left (y_{0} +\frac {22}{3}\right ) \]

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 39

ode=D[y[t],t]-3/2*y[t]==3*t+3*Exp[t]; 
ic={y[0]==y0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{3 t/2} \left (\int _0^t3 e^{-\frac {3 K[1]}{2}} \left (K[1]+e^{K[1]}\right )dK[1]+\text {y0}\right ) \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*t - 3*y(t)/2 - 3*exp(t) + Derivative(y(t), t),0) 
ics = {y(0): y__0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - 2 t + \left (y^{0} + \frac {22}{3}\right ) e^{\frac {3 t}{2}} - 6 e^{t} - \frac {4}{3} \]