63.4.23 problem 11

Internal problem ID [13066]
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
Date solved : Tuesday, January 28, 2025 at 04:51:03 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&={\mathrm e} \end{align*}

✓ Solution by Maple

Time used: 0.182 (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: 0.870 (sec). Leaf size: 21

DSolve[{D[x[t],t]==(4+2*t)*x[t]/Log[x[t]],{x[0]==Exp[1]}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{\sqrt {2 t^2+8 t+1}} \]