Internal problem ID [1947]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.1-3, page 6
Problem number: 1.1-3 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {{\mathrm e}^{t}}{y}=0} \end {gather*} With initial conditions \begin {align*} [y \left (\ln \relax (2)\right ) = -8] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 14
dsolve([diff(y(t),t)=exp(t)/y(t),y(ln(2)) = -8],y(t), singsol=all)
\[ y \relax (t ) = -\sqrt {2 \,{\mathrm e}^{t}+60} \]
✓ Solution by Mathematica
Time used: 0.6 (sec). Leaf size: 21
DSolve[{y'[t]==Exp[t]/y[t],y[Log[2]]==-8},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {2} \sqrt {e^t+30} \\ \end{align*}