Internal problem ID [14333]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y+\left (2 t -{\mathrm e}^{y} y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 34
dsolve(y(t)+(2*t-y(t)*exp(y(t)))*diff(y(t),t)=0,y(t), singsol=all)
\[ \frac {\left (-y \left (t \right )^{2}+2 y \left (t \right )-2\right ) {\mathrm e}^{y \left (t \right )}+t y \left (t \right )^{2}-c_{1}}{y \left (t \right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 32
DSolve[y[t]+(2*t-y[t]*Exp[y[t]])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [t=\frac {e^{y(t)} \left (y(t)^2-2 y(t)+2\right )}{y(t)^2}+\frac {c_1}{y(t)^2},y(t)\right ] \]