Internal problem ID [14188]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {5^{-t}}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 85
dsolve(diff(y(t),t)=5^(-t)/y(t)^2,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {\left (c_{1} \ln \left (5\right )-3 \,5^{-t}\right )^{\frac {1}{3}}}{\ln \left (5\right )^{\frac {1}{3}}} \\ y \left (t \right ) &= -\frac {\left (c_{1} \ln \left (5\right )-3 \,5^{-t}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2 \ln \left (5\right )^{\frac {1}{3}}} \\ y \left (t \right ) &= \frac {\left (c_{1} \ln \left (5\right )-3 \,5^{-t}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2 \ln \left (5\right )^{\frac {1}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.979 (sec). Leaf size: 88
DSolve[y'[t]==5^(-t)/y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt [3]{-\frac {3}{\log (5)}} \sqrt [3]{-5^{-t}+c_1 \log (5)} \\ y(t)\to \sqrt [3]{-\frac {3\ 5^{-t}}{\log (5)}+3 c_1} \\ y(t)\to (-1)^{2/3} \sqrt [3]{-\frac {3\ 5^{-t}}{\log (5)}+3 c_1} \\ \end{align*}