74.8.25 problem 25

Internal problem ID [16161]
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 : 25
Date solved : Tuesday, January 28, 2025 at 08:53:11 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} y^{\prime }+y&=\frac {{\mathrm e}^{t}}{y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 90

dsolve(diff(y(t),t)+y(t)=exp(t)/y(t)^2,y(t), singsol=all)
 

\begin{align*} y &= \frac {2^{{1}/{3}} {\left (\left (3 \,{\mathrm e}^{4 t}+4 c_{1} \right ) {\mathrm e}^{-3 t}\right )}^{{1}/{3}}}{2} \\ y &= -\frac {2^{{1}/{3}} {\left (\left (3 \,{\mathrm e}^{4 t}+4 c_{1} \right ) {\mathrm e}^{-3 t}\right )}^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y &= \frac {2^{{1}/{3}} {\left (\left (3 \,{\mathrm e}^{4 t}+4 c_{1} \right ) {\mathrm e}^{-3 t}\right )}^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 8.253 (sec). Leaf size: 96

DSolve[D[y[t],t]+y[t]==Exp[t]/y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {\sqrt [3]{3 e^t+4 c_1 e^{-3 t}}}{2^{2/3}} \\ y(t)\to -\frac {\sqrt [3]{-1} \sqrt [3]{3 e^t+4 c_1 e^{-3 t}}}{2^{2/3}} \\ y(t)\to \left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{3 e^t+4 c_1 e^{-3 t}} \\ \end{align*}