9.17.2 problem 2

Internal problem ID [3238]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 26, page 115
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 06:30:06 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+5 x \left (t \right )&=3 t^{2}\\ \frac {d}{d t}y \left (t \right )+y \left (t \right )&={\mathrm e}^{3 t} \end{align*}

✓ Maple. Time used: 0.154 (sec). Leaf size: 36

ode:=[diff(x(t),t)+5*x(t) = 3*t^2, diff(y(t),t)+y(t) = exp(3*t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= \frac {3 t^{2}}{5}-\frac {6 t}{25}+\frac {6}{125}+{\mathrm e}^{-5 t} c_2 \\ y \left (t \right ) &= \frac {{\mathrm e}^{3 t}}{4}+{\mathrm e}^{-t} c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.061 (sec). Leaf size: 50

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

\begin{align*} x(t)&\to \frac {3 t^2}{5}-\frac {6 t}{25}+c_1 e^{-5 t}+\frac {6}{125}\\ y(t)&\to \frac {e^{3 t}}{4}+c_2 e^{-t} \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 37

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

\[ \left [ x{\left (t \right )} = C_{1} e^{- 5 t} + \frac {3 t^{2}}{5} - \frac {6 t}{25} + \frac {6}{125}, \ y{\left (t \right )} = C_{2} e^{- t} + \frac {e^{3 t}}{4}\right ] \]