90.1.19 problem 30

Internal problem ID [25043]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 30
Date solved : Thursday, October 02, 2025 at 11:47:46 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=2 t +1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t) = 2*t+1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {1}{3} t^{3}+\frac {1}{2} t^{2}+c_1 t +c_2 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 26

ode=D[y[t],{t,2}]== 2*t+1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {t^3}{3}+\frac {t^2}{2}+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(-2*t + Derivative(y(t), (t, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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