Internal problem ID [1691]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.9. Page 66
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\frac {y^{2}}{2}-2 y \,{\mathrm e}^{t}+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.041 (sec). Leaf size: 39
dsolve(1/2*y(t)^2-2*exp(t)*y(t)+(-exp(t)+y(t))*diff(y(t),t) = 0,y(t), singsol=all)
\begin{align*} y \relax (t ) = \left (1-\sqrt {1+c_{1} {\mathrm e}^{-3 t}}\right ) {\mathrm e}^{t} \\ y \relax (t ) = \left (1+\sqrt {1+c_{1} {\mathrm e}^{-3 t}}\right ) {\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.885 (sec). Leaf size: 70
DSolve[1/2*y[t]^2-2*Exp[t]*y[t]+(-Exp[t]+y[t])*y'[t] == 0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t-\frac {\sqrt {-e^{3 t}-c_1}}{\sqrt {-e^t}} \\ y(t)\to e^t+\frac {\sqrt {-e^{3 t}-c_1}}{\sqrt {-e^t}} \\ \end{align*}