75.33.7 problem 836

Internal problem ID [17289]
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
Date solved : Tuesday, January 28, 2025 at 09:58:56 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=1 \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 8.650 (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: 0.028 (sec). Leaf size: 12

DSolve[{D[x[t],{t,2}]==1,{x[0]==0,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {t^2}{2} \]