Internal problem ID [15088]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 200.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {{y^{\prime }}^{2}-2 y y^{\prime }-y^{2} \left ({\mathrm e}^{2 x}-1\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x)^2-2*y(x)*diff(y(x),x)=y(x)^2*(exp(2*x)-1),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} {\mathrm e}^{x -{\mathrm e}^{x}} \\ y \left (x \right ) &= c_{1} {\mathrm e}^{x +{\mathrm e}^{x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 36
DSolve[y'[x]^2-2*y[x]*y'[x]==y[x]^2*(Exp[2*x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{x-e^x} \\ y(x)\to c_1 e^{x+e^x} \\ y(x)\to 0 \\ \end{align*}