56.1.57 problem 57

Internal problem ID [8769]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 57
Date solved : Monday, January 27, 2025 at 04:48:40 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

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

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

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