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 : Monday, January 27, 2025 at 07:36:21 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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