Internal problem ID [15559]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3. Section 24.2. Solving the Cauchy problem for linear differential equation with
constant coefficients. Exercises page 249
Problem number: 836.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {x^{\prime \prime }=1} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.343 (sec). Leaf size: 9
dsolve([diff(x(t),t$2)=1,x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {t^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 12
DSolve[{x''[t]==1,{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {t^2}{2} \]