66.6.12 problem 20

Internal problem ID [16024]
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 1.8 page 121
Problem number : 20
Date solved : Thursday, October 02, 2025 at 10:39:03 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=3 t^{2}+2 t -1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(y(t),t)+2*y(t) = 3*t^2+2*t-1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {3 t^{2}}{2}-\frac {t}{2}-\frac {1}{4}+{\mathrm e}^{-2 t} c_1 \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 40

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

\begin{align*} y(t)&\to e^{-2 t} \left (\int _1^te^{2 K[1]} \left (3 K[1]^2+2 K[1]-1\right )dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*t**2 - 2*t + 2*y(t) + Derivative(y(t), t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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