17.2.3 problem 1.1-3 (c)

Internal problem ID [3427]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (c)
Date solved : Tuesday, March 04, 2025 at 04:38:26 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \end{align*}

With initial conditions

\begin{align*} y \left (\ln \left (2\right )\right )&=-8 \end{align*}

✓ Maple. Time used: 0.080 (sec). Leaf size: 14

ode:=diff(y(t),t) = exp(t)/y(t); 
ic:=y(ln(2)) = -8; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\sqrt {2 \,{\mathrm e}^{t}+60} \]

✓ Mathematica. Time used: 0.574 (sec). Leaf size: 21

ode=D[y[t],t]==Exp[t]/y[t]; 
ic=y[Log[2]]==-8; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\sqrt {2} \sqrt {e^t+30} \]

✓ Sympy. Time used: 0.306 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - exp(t)/y(t),0) 
ics = {y(log(2)): -8} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \sqrt {2 e^{t} + 60} \]