Internal problem ID [10349]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{\prime \prime } t +x^{\prime }-1=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 0, x^{\prime }\left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 9
dsolve([diff(t*diff(x(t),t),t)=1,x(1) = 0, D(x)(1) = 2],x(t), singsol=all)
\[ x \left (t \right ) = \ln \left (t \right )+t -1 \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 10
DSolve[{D[t*x'[t],t]==1,{x[1]==0,x'[1]==2}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t+\log (t)-1 \\ \end{align*}