Internal problem ID [14407]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {{\mathrm e}^{5 t}}{y^{4}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 144
dsolve(diff(y(t),t)=exp(5*t)/y(t)^4,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \left ({\mathrm e}^{5 t}+c_{1} \right )^{\frac {1}{5}} \\ y \left (t \right ) &= -\frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}+\sqrt {5}+1\right ) \left ({\mathrm e}^{5 t}+c_{1} \right )^{\frac {1}{5}}}{4} \\ y \left (t \right ) &= \frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}-\sqrt {5}-1\right ) \left ({\mathrm e}^{5 t}+c_{1} \right )^{\frac {1}{5}}}{4} \\ y \left (t \right ) &= -\frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}-\sqrt {5}+1\right ) \left ({\mathrm e}^{5 t}+c_{1} \right )^{\frac {1}{5}}}{4} \\ y \left (t \right ) &= \frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}+\sqrt {5}-1\right ) \left ({\mathrm e}^{5 t}+c_{1} \right )^{\frac {1}{5}}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.921 (sec). Leaf size: 117
DSolve[y'[t]==Exp[5*t]/y[t]^4,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt [5]{e^{5 t}+5 c_1} \\ y(t)\to -\sqrt [5]{-1} \sqrt [5]{e^{5 t}+5 c_1} \\ y(t)\to (-1)^{2/5} \sqrt [5]{e^{5 t}+5 c_1} \\ y(t)\to -(-1)^{3/5} \sqrt [5]{e^{5 t}+5 c_1} \\ y(t)\to (-1)^{4/5} \sqrt [5]{e^{5 t}+5 c_1} \\ \end{align*}