10.1.31 problem 31

Internal problem ID [1128]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 31
Date solved : Saturday, March 29, 2025 at 10:40:39 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = -2 t -\frac {4}{3}-4 \,{\mathrm e}^{t}+{\mathrm e}^{\frac {3 t}{2}} c_1 \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 27

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

\[ y(t)\to -2 t-4 e^t+c_1 e^{3 t/2}-\frac {4}{3} \]

✓ Sympy. Time used: 0.144 (sec). Leaf size: 22

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

\[ y{\left (t \right )} = C_{1} e^{\frac {3 t}{2}} - 2 t - 4 e^{t} - \frac {4}{3} \]