56.1.56 problem 56

Internal problem ID [8768]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 56
Date solved : Monday, January 27, 2025 at 04:48:39 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \int \left (\int f \left (t \right )d t \right )d t +c_{1} t +c_{2} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 30

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

\[ y(t)\to \int _1^t\int _1^{K[2]}f(K[1])dK[1]dK[2]+c_2 t+c_1 \]