Internal problem ID [14427]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {y^{\prime }+y-\frac {{\mathrm e}^{t}}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 92
dsolve(diff(y(t),t)+y(t)=exp(t)/y(t)^2,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {2^{\frac {1}{3}} {\left (\left (3 \,{\mathrm e}^{4 t}+4 c_{1} \right ) {\mathrm e}^{-3 t}\right )}^{\frac {1}{3}}}{2} \\ y \left (t \right ) &= -\frac {2^{\frac {1}{3}} {\left (\left (3 \,{\mathrm e}^{4 t}+4 c_{1} \right ) {\mathrm e}^{-3 t}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4} \\ y \left (t \right ) &= \frac {2^{\frac {1}{3}} {\left (\left (3 \,{\mathrm e}^{4 t}+4 c_{1} \right ) {\mathrm e}^{-3 t}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.499 (sec). Leaf size: 96
DSolve[y'[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*}