Internal problem ID [10372]
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: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-\frac {\left (4+2 t \right ) x}{\ln \left (x\right )}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = {\mathrm e}] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 17
dsolve([diff(x(t),t)=(4+2*t)*x(t)/ln(x(t)),x(0) = exp(1)],x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{\sqrt {2 t^{2}+8 t +1}} \]
✓ Solution by Mathematica
Time used: 0.904 (sec). Leaf size: 19
DSolve[{x'[t]==(4+2*t)*x[t]/Log[x[t]],{x[0]==Exp[1]}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{\sqrt {2 t (t+4)+1}} \\ \end{align*}