57.4.23 problem 11

Internal problem ID [14347]
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 : Thursday, October 02, 2025 at 09:32:05 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*}

✓ Maple. Time used: 0.092 (sec). Leaf size: 17

ode:=diff(x(t),t) = (4+2*t)*x(t)/ln(x(t)); 
ic:=[x(0) = exp(1)]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = {\mathrm e}^{\sqrt {2 t^{2}+8 t +1}} \]

✓ Mathematica. Time used: 0.507 (sec). Leaf size: 21

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

\begin{align*} x(t)&\to e^{\sqrt {2 t^2+8 t+1}} \end{align*}

✓ Sympy. Time used: 1.275 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((-2*t - 4)*x(t)/log(x(t)) + Derivative(x(t), t),0) 
ics = {x(0): E} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = e^{\sqrt {2} \sqrt {t^{2} + 4 t + \frac {1}{2}}} \]