68.11.11 problem 23

Internal problem ID [17548]
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 : 23
Date solved : Thursday, October 02, 2025 at 02:25:18 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=3 t^{4}-2 t \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(y(t),t),t) = 3*t^4-2*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {1}{10} t^{6}-\frac {1}{3} t^{3}+\frac {5}{18}+c_1 t +c_2 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

ode=D[y[t],{t,2}]==3*t^4-2*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {t^6}{10}-\frac {t^3}{3}+c_2 t+c_1 \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*t**4 + 2*t + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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