Internal problem ID [6347]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 56.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-f \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(diff(y(t),t$2)=f(t),y(t), singsol=all)
\[ y \relax (t ) = \int \left (\int f \relax (t )d t \right )d t +t c_{1}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 30
DSolve[y''[t]==f[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \int _1^t\int _1^{K[2]}f(K[1])dK[1]dK[2]+c_2 t+c_1 \\ \end{align*}