Internal problem ID [957]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-2 y-\frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 84
dsolve(diff(y(x),x)-2*y(x)=x*exp(2*x)/(1-y(x)*exp(-2*x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \left ({\mathrm e}^{-2 x}+\sqrt {-{\mathrm e}^{-4 x} x^{2}-2 \,{\mathrm e}^{-4 x} c_{1}+{\mathrm e}^{-4 x}}\right ) {\mathrm e}^{4 x} \\ y \relax (x ) = -\left (-{\mathrm e}^{-2 x}+\sqrt {-{\mathrm e}^{-4 x} x^{2}-2 \,{\mathrm e}^{-4 x} c_{1}+{\mathrm e}^{-4 x}}\right ) {\mathrm e}^{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.937 (sec). Leaf size: 72
DSolve[y'[x]-2*y[x]==x*Exp[2*x]/(1-y[x]*Exp[-2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x}-\frac {\sqrt {x^2-1-c_1}}{\sqrt {-e^{-4 x}}} \\ y(x)\to e^{2 x}+\frac {\sqrt {x^2-1-c_1}}{\sqrt {-e^{-4 x}}} \\ \end{align*}