15.18.1 problem 1

Internal problem ID [3244]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:27:21 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

\[ y = -\cos \left (t \right )+c_{1} t +c_2 \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 16

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

\[ y(t)\to -\cos (t)+c_2 t+c_1 \]