56.1.55 problem 55

Internal problem ID [8767]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 55
Date solved : Wednesday, March 05, 2025 at 06:46:14 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {1}{2} t^{2}+c_{1} t +c_{2} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

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

\[ y(t)\to \frac {t^2}{2}+c_2 t+c_1 \]

✓ Sympy. Time used: 0.052 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), (t, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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