72.6.14 problem 22

Internal problem ID [14668]
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 : 22
Date solved : Monday, March 31, 2025 at 12:52:09 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=t^{3}+\sin \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 35

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

\[ y = t^{3}-3 t^{2}+6 t -6-\frac {3 \cos \left (3 t \right )}{10}+\frac {\sin \left (3 t \right )}{10}+{\mathrm e}^{-t} c_1 \]

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 36

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

\[ y(t)\to e^{-t} \left (\int _1^te^{K[1]} \left (K[1]^3+\sin (3 K[1])\right )dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.171 (sec). Leaf size: 36

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

\[ y{\left (t \right )} = C_{1} e^{- t} + t^{3} - 3 t^{2} + 6 t + \frac {\sin {\left (3 t \right )}}{10} - \frac {3 \cos {\left (3 t \right )}}{10} - 6 \]