63.3.3 problem 3

Internal problem ID [13038]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.2 Antiderivatives. Exercises page 19
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 04:49:55 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=-3 \sqrt {t} \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=4\\ x^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 14

dsolve([diff(x(t),t$2)=-3*sqrt(t),x(1) = 4, D(x)(1) = 2],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {4 t^{{5}/{2}}}{5}+4 t +\frac {4}{5} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 19

DSolve[{D[x[t],{t,2}]==-3*Sqrt[t],{x[1]==4,Derivative[1][x][1 ]==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\frac {4}{5} \left (t^{5/2}-5 t-1\right ) \]