66.1.16 problem 19

Internal problem ID [15903]
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 1.2. page 33
Problem number : 19
Date solved : Thursday, October 02, 2025 at 10:29:36 AM
CAS classification : [_separable]

\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ v = -1+{\mathrm e}^{\frac {t \left (t^{2}-6\right )}{3}} c_1 \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 27

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

\begin{align*} v(t)&\to -1+c_1 e^{\frac {1}{3} t \left (t^2-6\right )}\\ v(t)&\to -1 \end{align*}

✓ Sympy. Time used: 0.206 (sec). Leaf size: 15

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

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