68.11.50 problem 62 (a)

Internal problem ID [17587]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 62 (a)
Date solved : Thursday, October 02, 2025 at 02:25:53 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-4 y&=t^{2} \end{align*}

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

ode:=diff(y(t),t)-4*y(t) = t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {t^{2}}{4}-\frac {t}{8}-\frac {1}{32}+{\mathrm e}^{4 t} c_1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 32

ode=D[y[t],t]-4*y[t]==t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{4 t} \left (\int _1^te^{-4 K[1]} K[1]^2dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2 - 4*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{4 t} - \frac {t^{2}}{4} - \frac {t}{8} - \frac {1}{32} \]