Internal problem ID [10378]
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 1.3.1 Separable equations. Exercises page
26
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\frac {x^{\prime \prime } t +x^{\prime }}{t}+2=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(1/t*diff(t*diff(x(t),t),t)=-2,x(t), singsol=all)
\[ x \left (t \right ) = -\frac {t^{2}}{2}+\ln \left (t \right ) c_{1} +c_{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 20
DSolve[1/t*D[t*x'[t],t]==-2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {t^2}{2}+c_1 \log (t)+c_2 \\ \end{align*}