56.1.55 problem 55

Internal problem ID [8767]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 55
Date solved : Monday, January 27, 2025 at 04:48:36 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)=1,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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