Internal problem ID [10343]
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: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-\frac {1+t}{\sqrt {t}}=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(x(t),t)=(1+t)/sqrt(t),x(1) = 4],x(t), singsol=all)
\[ x \left (t \right ) = \frac {2 t^{\frac {3}{2}}}{3}+2 \sqrt {t}+\frac {4}{3} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 20
DSolve[{x'[t]==(1+t)/Sqrt[t],{x[1]==4}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {2}{3} \left (\sqrt {t} (t+3)+2\right ) \\ \end{align*}