67.5.10 problem Problem 2(e)

Internal problem ID [14017]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 2(e)
Date solved : Wednesday, March 05, 2025 at 10:26:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=3 t^{2} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

ode:=3*diff(diff(y(t),t),t)+5*diff(y(t),t)-2*y(t) = 3*t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {3 \,{\mathrm e}^{-2 t} \left (-\frac {2 \,{\mathrm e}^{\frac {7 t}{3}} c_{2}}{3}+\left (t^{2}+5 t +\frac {31}{2}\right ) {\mathrm e}^{2 t}-\frac {2 c_{1}}{3}\right )}{2} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 38

ode=3*D[y[t],{t,2}]+5*D[y[t],t]-2*y[t]==3*t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {3}{4} \left (2 t^2+10 t+31\right )+c_1 e^{t/3}+c_2 e^{-2 t} \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*t**2 - 2*y(t) + 5*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{\frac {t}{3}} - \frac {3 t^{2}}{2} - \frac {15 t}{2} - \frac {93}{4} \]