Internal problem ID [10344]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {x^{\prime \prime }+3 \sqrt {t}=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 4, x^{\prime }\left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve([diff(x(t),t$2)=-3*sqrt(t),x(1) = 4, D(x)(1) = 2],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {4 t^{\frac {5}{2}}}{5}+4 t +\frac {4}{5} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 19
DSolve[{x''[t]==-3*Sqrt[t],{x[1]==4,x'[1]==2}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {4}{5} \left (t^{5/2}-5 t-1\right ) \\ \end{align*}